I like using a Dremel tool with a grinding stone bit. Another option is to get a sharpening kit. I'm sure lawnmower and tool sharpening shops would offer this service too.

Here is a link that might be useful: Sharpening Kit

Do not use a dremel tool or any other kind of grinding device to attempt to sharpen your reel. Reel grinding is a very complicated procedure. If you try to grind your reel by hand the reel and bedknife will NEVER mate together properly again. I don't know what mower shops are pushing these "reel sharpenings" but grinding the reel is something that should rarely if ever need to be done to a homeowners walk-behind. Learn how to frequently and competantly adjust your reel to bedknife clearance. Backlap twice a season if you want to. Unless you damage the edge by running something over that is very hard, or your cut is streaking, you should never need to have your reel ground.