Please keep in mind that the following info is from my personal 30+ year tile painting experiences. Other painters have their own good advice to share.

What You Will Need
Assuming you don't own a kiln, make sure you locate someone who will fire your work, before purchasing supplies. Most Ceramic stores do low temp fires occasionally, but phoning several places may be necessary.
I buy most of my supplies from Rynne China Co. , 222 West Eight Mile Road, Hazel Park, Michigan.48030 (phone: 1-800-468-1987) and Rosebud, PO Box 1051, Orchard Park, NY 14127. I have found them to be reliable sources of high quality paints. Rosebud also makes available a Color Mixing Chart that comes in quite handy.
Or you might want to call Ceramic outlets in your area, they may carry powdered china paints.

Decide upon the subject of your painting. Make lots of sketches, refine the sketch you want to paint on graph paper . Mark your graph paper with the exact size of the tile/tiles you will be working on.

Buy only the color paints needed for your first project. The paints I use are called Overglaze (or china) Paints in Powder Form. They come in half dram glass vials or by the ounce in paper envelopes. Even though it is more expensive, buy in the glass vials until you find out what colors you like using. A little goes a long way. I find that in painting animals I use a lot of Best Black, Hair Brown, Rembrandt Brown and Tan but there are many colors to choose from. Reds and purples are difficult to use so try to avoid the need for now. Don't plan on using White. Any white highlights will be the tile not paint. You can't be sure of the results when trying to mix colors, so save that experimentation for later. If your design needs yellow and red or purple, it would be safest to use Yellow for Mixing for now.

Same for the tiles, buy only what you need (plus three extra: two for mixing paints and one in case of accidents). Most places like "Tile Mart" will sell individual tiles so you aren't stuck with a mess of them. Buy plain shiny white glazed ceramic tiles. Sometimes the thin cheaper tiles are the best! but if you want to be sure you are getting a quality tile that most likely won't surprise you in the fire, buy from Rynne China or Daltile (Semi-gloss wall tile). Don't be tempted by the colored or textured ones, you can't tell what your results will be. Clean your tiles with soapy water, rinse and allow to dry thoroughly. You will mix your paints with oil (I recommend using Rynne's Painting Mixing Medium) and turpentine (I use odorless turpenoid which is available at most drug, art or craft stores).
For now you will only need to purchase 1 small and 2 medium oil painting brushes and a small palette knife. (If you are going to start with a subject that is large and hairy, also buy a large brush.) Buy good but not overly expensive brushes. You don't want hairs to fall out into your work, but you also shouldn't have to worry about ruining an expensive brush. Only use new brushes, any residue from other types of paint will ruin your finished piece. A wipe-out tool is handy but I have often used a wooden skewer or the wooden tip of a paintbrush instead.