This should be a fairly easy project for you. The first step it to determine, if possible, if the existing paint is an oil or latex based paint. If you have the bucket that the old paint was in, you're in luck. Otherwise, it is hard to tell even though a trained eye may be able to tell. Regardless, using latex will be safe over either oil or latex (oil over latex will wrinkle and peel almost immediately and make a mess).
Since black will be hard to cover with one or two coats of white, I'd use a good blocking primer like Kilz or any good color block. Two quick coats of primer should be a great backer for white over black. Then just roll on your good quality, hard finish floor latex enamel. Probably two coats will do the trick.
Be sure to clean the existing black finish well, and if possible, sand lightly just to rough up the surface a bit. This will help assure a good bond with the primer. Good luck.