If you use primer first, that'll cover the black and provide a good base coat to spray a lighter color on. They sell primer spraypaint in the same place they sell regular spraypaint; just choose a plain-color primer, like gray, so it's easy to cover w/ your main color.
It will probably take severaI coats of your main color to get a good finish, whether you use primer or not, so just allow enough time for each coat to dry (follow the dry time it says on the can). You may need to sand in between coats if the paint runs in places (which will happen if you go too heavy on the paint in an area); purchase a finer-grit sandpaper, something between 150 to 250 grit (the higher the number, the finer / gentler the grit). After a coat has dried, you can sand down any bad spots, wipe it down to get the dust off, and hit it w/ another coat of paint. You probably will want to paint the whole piece each time you put a coat on there, so the finish will be uniform on the whole piece.
Usually the lighter the color, the more coats you'll need. If you paint them red or blue, that should only take 2-3 coats; if you decide to paint them yellow, that may take an extra coat or two to make it look nice.
And paint outside so you're not breathing all the fumes! It takes a little practice and trial and error, but it's fairly easy once you get the hang of it.