You can simply tape a credit card or even an index card over the feed dogs to cover them. Punch a small hole in the card for the needle to go through.
Do you want to cover the feed dogs in order to do free motion quilting? If so, you will need a darning foot ("jumping" type foot). You can try FMQ with the feed dogs up; some quilters find this actually works better for them than dropping or covering up the feed dogs. It depends a lot on the individual machine.
Most machines are short-shank. It's pretty easy to find a 1/4-inch screw-on foot for a short-shank machine. However, I find most of those feet are not sufficiently accurate for me (the inattentive klutz). What I do instead is make a physical guide at the scant 1/4-inch point with a strip of adhesive moleskin (purchased in the foot area of any pharmacy).
Here is a link that shows how to determine the shank type of your machine:
http://www.clotilde.com/pages/which_foot.html