I have a Nikon D5100 and want to find a telephoto adapter that go with my 55-300mm lens, which has a 58mm filter thread. Most I see are 52mm — why is that? What should I be looking for to FIT my 300mm lens?
Most of the add-on "teleconverter" filters that are 52mm are designed to be used with fixed-lens cameras, not interchangeable lens cameras. It's common for bridge cameras to either have a 52mm or 58mm filter thread, or to allow for an accessory tube that attaches bayonet-style to add a filter thread.
With a dSLR, the more common type of teleconverter to use is one that mounts between the rear of the lens and the camera. The glass tends to be of higher quality than screw-on converters, and they may report and pass through electronic signals from the body to the lens, so they are more expensive.
When you introduce an additional element to a lens that isn't part of the lens's design, you tend to reduce the image quality. And in the case of teleconverters that increase the effective focal length of the lens, you'll also be reducing the maximum aperture--possibly to the point where you'll lose autofocus with your camera body. For example, a 2x teleconverter adds two stops to the maximum aperture, and most entry-level bodies (like your D5100) tend to stop autofocusing or have much wonkier autofocusing if the maximum aperture goes past f/8. The maximum aperture determines how much light hits the AF sensor array, the darker it gets, the harder it is for the AF to lock. The 55-300 being an f/4.5-5.6 lens with a 2x tc would become an f/9-f/11 lens.
As someone who occasionally throws a 1.4x tc onto a 400mm f/5.6 prime lens, I will say that adding a teleconverter is a compromise. It will not perform the way a longer lens will. Granted, it's far less expensive, and you do gain reach, but most of the savings come at the cost of sharpness and autofocus performance.