First, wash and moisturize your face. These are the products I use, but you can use whatever you have. This applies for everything from here on out. I will post my products. Use what you like.
Next, apply a primer. Do not skip this step. Primer is super important to get your makeup to apply nicely, stay, and last.
Next step, apply your foundation. I recommend a cream or BB foundation for cosplaying because it will show up flawless in pictures. A regular liquid is probably not going to give you the coverage you need. Then, concealer! Unless you have perfect skin, use concealer. You may not need a lot like I do, but use it. Also, use green first, then skin color. Green will help mask the redness of a blemish or scar. If you have dark circles under your eyes, use the skin color to conceal.
Get yourself some makeup brushes (and make sure you clean them regularly!) and use a large brush to apply powder over your entire face.
Now, for the mouth. I recommend using a reference picture, but feel free to make it your own. You are welcome to use my final picture as your reference, or the one I used:
I bought some cheap face paint (huge package with multiple colors) at Walmart and that's what I used. Using black, and a small paint brush, outline the mouth. Then, outline the teeth.
Fill in the black between upper and bottom teeth.
For the teeth: First, use a white eye liner pencil and fill in the teeth. Then, go over it using the face paint.
I used eyeshadow to deepen the black and soften the upper and lower jaw lines. I also used white eye shadow to fill in the teeth a bit.
Now for the eyes. I decided I wanted to try a purple lid with hot pink accent and highlight. You can do whatever you want. First, use an eye shadow primer.
Next, use a white eye liner pencil and cover your entire eyelid where you plan to put color. This will help the color really pop!
Next, add the pink. Then, blend.
Next, use black liquid eyeliner (if you aren't good at liquid eyeliner, buy some and practice! First couple of times will look like crap, but I picked it up fairly quickly just by doing it). Top and bottom.
Add mascara and you're finished! If you want, you can add falsies to really pop the eyes and contacts for a more cat like look. I used blue circle lens' because 1) it's what I already had and 2) the Cheshire Cat doesn't actually have cat eyes in the original movie. Add your wig and costume and you are good to go!
FYI, the wig is a cheapo Halloween one that I styled. Simply back combed and added braids of all kinds to give it a Steampunk feel. Good luck and happy cosplaying!