First, I'd rub some cornstarch into the stains with an old toothbrush. Leave it on overnight. Brush off surface constarch with the toothbrush and see how much of the grease the cornstarch absorbed. Then - take a bar of plain Ivory soap
take a wet, clean, light colored cloth and rub some Ivory onto the cloth. Rub the stain with plenty of Ivory. Now, you can do one of two things: 1. keep scrubbing the spot(s) with the Ivory until you see the stain lighten or disappear or
2. rub the Ivory into the stain then leave it for awhile, then do step one. Leaving the soap in for a while allows it to absorb the stain and makes it easier to rub out(it doesn't hurt if the soap dries on the fabric). After cleaning with the soap, you should rinse by rubbing with a clean, wet cloth. You can skip the cornstarch and just do the Ivory routine if you want.
Holding or placing a dry towel under the area you're working on will absorb the excess water and help it dry faster. You can also use a blow dryer to dry faster. If after drying there is a ring, that's soap residue and can easily be rinsed out by rinsing again. I find this works on 90% of stains and does very well even on oil or grease stains.