A simple way to increase the magnification of your telephoto lens is to use a teleconverter (which we’ll often abbreviate as TC).  These are compact optical devices that attach to your lens (between the lens and the camera) and magnify the resulting image by a factor of either 1.4×, 1.7×, 2×, or even (in rare cases) 3×.  An example of a 1.4× TC and a 2× TC are shown below. 



When attached to a lens having a focal length of F, a 1.4× TC results in an effective focal length of 1.4×F, whereas a 2× TC results in an effective focal length of 2×F.  Thus, a 400mm lens with a 1.4× teleconverter attached provides the same magnification as a 560mm lens, since 1.4 × 400 = 560.  Similarly, a 400mm lens with a 2× converter produces the same magnification as a true 800mm lens. 
    For birders, teleconverters can be a godsend.  For warbler-sized birds foraging high in the trees, even a 500mm or 600mm lens will generally prove inadequate for capturing significant feather detail in the bird.  By attaching a 1.4× TC, these 500mm or 600mm lenses become 720mm or 840mm lenses, respectively.  As we’ll see below, teleconverters can even be stacked—meaning that you can attach several TC’s in tandem to achieve even higher magnification.  And because TC’s are fairly easy to put on and take off, they give you some flexibility in the field for varying your focal length even if you’re using a prime lens (i.e., not a zoom).
    Unfortunately, in photography (as in many things) there is no free lunch.  Any teleconverter that results in an increased focal length will also result in a reduced aperture, and the reason for this is simple: since the f-number of a lens is defined as F/d, for focal length F and objective diameter d, increasing F without also increasing d will result in a higher f-number, which corresponds to a smaller aperture (and therefore darker images, or slower shutter speeds, or higher ISO...).  To continue with the examples above, a 400mm f/5.6 lens fitted with a 1.4× TC will behave like a 560mm f/8 lens, because:


Similarly, with a 2× TC the 400mm f/5.6 lens becomes an 800mm f/11 lens, since 2 × 5.6 ≈ 11.  Thus, if your teleconverter provides a magnification factor of M (where M may be 1.4, 1.7, 2, etc.), and your lens has a focal length of F and an f-number of N, then the result of attaching the TC to the lens is to produce an effective focal length of M × F and an f-number of M × N.
    One practical consequence of this is that if your lens has a maximum aperture of f/5.6 or smaller (meaning that it has an f-number of 5.6 or higher), then you most likely won’t be able to use autofocus when using a teleconverter with that lens.  This is because virtually all consumer-grade and pro-sumer camera bodies refuse to autofocus at apertures smaller than f/5.6—and this means the effective aperture, after taking into account the TC.  Thus, for non-pro bodies, you’ll lose the ability to autofocus if you attach a 1.4× TC to any lens slower than f/4, or if you attach a 2× TC to any lens slower than f/2.8.  For pro bodies, which typically autofocus at f/8 or faster, you can use a 1.4× TC with any lens that’s f/5.6 or faster, or use a 2× TC with any lens that’s f/4 or faster. 
    In practice, if ambient light levels are very low, autofocus may become slow or inaccurate or even refuse to operate even at effective apertures that normally would retain autofocus capability.  A well-known trick, known as taping the pins, is to put a piece of tape or any other thin insulator over several of the electrical pins on the TC which allow the camera to communicate with the lens.  For some camera systems and some TC’s, taping the appropriate pins will trick the camera into thinking that the TC isn’t present, and that the effective aperture is wider than it really is.  Some third-party TC’s don’t even provide all the internal electrical connections between camera and lens, so that taping the pins isn’t even necessary with these TC’s.  As a result, the camera will attempt to autofocus even if the effective aperture is smaller than f/5.6 (or smaller than f/8 on a pro camera).  In practice, since the aperture really is smaller than what the camera thinks, autofocus accuracy and speed can be significantly impacted, and in some cases taping the pins might even lead to inadvertent damage to your lens or camera, due either to electrical short-circuiting or to over-use of the lens’ focusing motor as the camera tries in vain to find a proper focus.
    Although autofocus may become disabled, you can still use a teleconverter as long as you don’t mind focusing your lens manually.  For the eagle photo below, I was using a 600mm f/4 lens with a 2× TC, resulting in an effective focal length of 1200mm at f/8.  Although my pro camera body readily agreed to autofocus this configuration, I decided to manually focus instead, since I was afraid the autofocus would incorrectly lock onto one of the small twigs in front of the birds. 



As the image above demonstrates, the use of extreme focal lengths (1200mm in this case) can be highly useful, even essential, when photographing sensitive species that you can’t get very close to.  In this case, not only was I manually focusing (which often leads to suboptimal sharpness in bird images) and using an extreme focal length (at which minute vibrations in the camera or lens will be magnified to produce image blur), but I was using a 2× converter, which typically involves a nontrivial loss of image sharpness.  All teleconverters degrade image quality, though high end 1.4× TC’s (such as Canon’s 1.4× Extender II, which runs about US $380) when used with high-quality prime lenses typically produce very, very good image quality.  2× converters, on the other hand, regardless of make or price, typically degrade image quality quite noticeably. 
    For the image below, I was again using a 600mm f/4 lens with a 2× converter, though this time I relied on autofocus, and didn’t crop the image quite as aggressively in post-process.  It’s remarkable that, though I was about 200 feet away from these hawk chicks, you can see the individual filaments of downy feathers standing up on the birds’ heads.  This is partly due to the strong contrast imparted by the overhead light and the dark background, as well as to the application of a sharpening filter in post-process, but it demonstrates that detailed images can be obtained with 2× converters at fairly long distances with premium-quality optics. 



Even so, you’ll note that some distortion is present in the lower half of the image above, particular in the lower corners.  With a lower quality TC or lower quality prime (or even zoom) lens, the overall image quality could be drastically worse, and as a general rule I try not to use any 2× TC on any lens unless it’s absolutely necessary.
    For the truly fearless photographer working at extreme distances to small birds, it’s even possible to obtain reasonably sharp images when stacking teleconverters—that is, when using multiple teleconverters attached to the same lens at the same time.  For the image below, I use a 400mm f/4 lens with a 1.4× TC and a 2× TC attached, resulting in an effective focal length of 1120mm (1.4 × 2 × 400) and an effective aperture of f/11 (1.4 × 2 × 4 ≈ 11).



Although the above image may appear reasonably sharp, it’s been sharpened in post-process, and hasn’t been cropped much from the original image.  The use of teleconverters (even just one at a time) often reduces your ability to effectively crop an image, since image degradation introduced by the TC becomes more evident when zooming in on the image during post-processing.  For the above photo, further cropping (i.e., digital zooming) resulted in an awful-looking image, and I’d guess that prints of this image any larger than 5"×7" would look pretty terrible.
    For high-quality prime lenses, a good 1.4× TC should produce reasonably sharp images when used properly.  The warbler image below was shot at 840mm using a 1.4× TC on a 600mm f/4 lens.  With some sharpening in Photoshop I was able to bring out quite a lot of minute feather detail in this typically restless bird.




As yet another example of what’s possible with a quality teleconverter attached to a prime lens, the image below was again shot at 840mm (600mm + 1.4× TC), but this time without any tripod or other rigid support—in other words, this photo was shot hand-held using an enormous lens with a teleconverter attached (!).  Though there are some signs of artificial sharpening in this image, it’s at least a testament to the amount of detail that a prime lens with a good TC can capture.  Note that this image was fairly heavily cropped, so that the original RAW image contained quite a bit more background, especially on either side of the bird (the image was shot in landscape rather than portrait orientation, and then cropped to portrait).




    Now to show you just how bad teleconverters can be, the owl photo below was taken using the Nikon 80-400mm f/5.6 zoom lens with a cheap ($59), third-party 2× teleconverter attached.  The image was taken with an older, 6 MP camera, and was cropped a bit in post-process, so some of the problems with the image probably stem from the camera rather than from the TC.  But the overall lack of sharpness and contrast (even after post-processing) is most likely due to the poor optical quality of the TC.



    Another useful accessory for shooting birds with telephoto lenses is the extension tube.  These small devices outwardly resemble a teleconverter, but without any glass elements.  Whereas a teleconverter will typically contain 5-10 glass elements which magnify the image, an extension tube is just an empty tube containing nothing but air—basically like a plastic doughnut with a camera mount on the one side and a lens mount on the other.  Just like with teleconverters, they mount between your camera and your lens.




As you can see with the Canon extension tubes shown above, these tubes contain the metal pins which allow the camera to communicate electronically with the lens, to allow autofocus and control of the lens’ iris and (if present) image stabilizer.  Nikon’s extension tubes, on the other hand, lack these pins, so that when using the Nikon tubes you’ll have to autofocus manually (though third-party tubes for Nikon cameras are available, which do allow autofocus).
    The purpose of an extension tube is to reduce the minimum focus distance (MFD) of your lens.  Large-focal-length lenses in the 600mm to 800mm range typically have an MFD of 20 feet or more, so that if you try to focus on a bird only 15 feet away, the camera will refuse to focus.  An extension tube will reduce the MFD, sometimes by as much as 5 feet or more, and since tubes can be stacked, you can sometimes reduce the MFD quite drastically.  Although I used to use extension tubes quite a lot with my 800mm lens, I’ve stopped doing so, since they have several drawbacks.  Although an extension tube doesn’t affect the aperture like a teleconverter (or does so by a negligible amount), they do stop you from focusing on distant objects.  Thus, if you put on an extension tube to focus on a bird that’s very close, and then soon thereafter encounter a bird high up in a tree that you want to shoot, you’ll have to take off the tube before shooting the more distant bird, because with the tube connected, the lens loses the ability to focus on more distant subjects.
    Another drawback of extension tubes is that they can confuse the autofocus system in your camera, because they affect the focal length of the lens (very slightly—not enough to provide any useful magnification).  Recall from section 2.6 that the autofocus systems in DSLR’s use a clever trick to compute the exact amount by which they need to move the focusing element in the lens in order to achieve focus.  The introduction of extension tubes will slightly change the amount that the focuser needs to move, since they effectively move the focal point of the lens by a few millimeters.  As a result, unless the camera knows the tube is attached and compensates for this, the camera will tend to back-focus slightly.  In newer DSLR’s this can be compensated for by dialing in a microadjust setting (see section 3.11) to eliminate the back-focus issue.
    Instead of extension tubes, I now keep a second camera with a shorter-focal-length lens (and much closer MFD) slung over my left shoulder, so that if a bird approaches closer than what my tripod-mounted lens can focus on (approximately 18 feet), I can quickly switch to the other camera/lens combination, which focuses down to about 11 feet.  I’ve found this to work well in practice. 
    Note that some third-party extension tubes have a reputation for spontaneously disconnecting from either the camera or the lens.  With a tripod-mounted setup, this can result in your camera falling off the lens and possibly sustaining damage when it hits the ground.