I really want to take a picture of the Milky Way using my camera. I'm not sure if it is able to pick it up? The lens I am currently using is a Canon EF 55-200mm. Should I be able to this?
While it's definitely possible to capture the Milky with that lens, I would highly recommend something fast and wide. I recommend f/2.8 but you could probably get away with f/3.5. The problem is that you need to let in a lot of light for the Milky Way to be visible and the wider the aperture, the easier this is. You're 55-200mm lens might be too narrow for this use. If you're looking for a cheap lens to do the job, you might be able to get away with the 18-55mm Canon kit lens that comes with beginner DSLR's.
Obviously you're going to need a tripod since your exposure time is going to be rather long. I also recommend using live view if possible since focusing using the viewfinder in the dark is a pain.
Choosing the correct shutter speed can be tricky. The earth is spinning pretty dang fast so leave open to long and you're going to get star trails. I recommend using the 500 rule.
The crop factor varies from camera to camera but for Canon I believe it's 1.6.
Shoot at the highest ISO possible without introducing any noticeable noise. Once again, you need all the light you can get. Also, be sure to shoot away from cities, homes, etc... The ambient light will distract from the picture and most likely ruin it. (The moon can also do this.)
I did a quick Google search and found this: How to see the Milky Way. It's not always visible in all the parts of the world, so be sure you known where to be when it's visible.