As a guy who spent close to thirty years in the tile and stone business, including selling stone restoration products, I can tell you from experience that removing stains from stone is an exercise in patience. Concrete stain removal methods are very similar. Chance are, it will take multiple attempts to remove the stain completely, but it usually can be done.
Those who mentioned kitty litter and absorbents are on the right track. Using a poultice is a matter of redissolving the stain with (depending on the stain) a detergent or solvent, and then pulling it back out with the absorbent media. Cat litter, baking soda, powdered hobby clay, and talcum powder are the most commonly used media. Cat litter does work better if it is crushed up, you really want something close to a powder.
You can start with a detergent and some water, scrub it in to the stain, and leave it just surface damp; don't leave any standing water. Sprinkle a generous layer of absorbent over the water, enough so you can't see the moisture on the concrete. Then tape a sheet of plastic over the whole thing, at least 3 inches outside of the edge of the stain. Neatness counts when spreading the media, the tape won't stick to any stray powder. When the plastic is all taped down securely, leave it.
Come back in a day or two and if the powder looks dry, or feels crusty if you poke it with a finger under the plastic sheeting, you can peel back the plastic and sweep up the powder. If it still feels soft and punky, leave it until it dries.
Now look at your stain. If it looks lighter, the poultice is working. You can go at it again with the same treatment. If it looks no different, try again, this time with a stronger concentration of cleaner or move on to a solvent. Use fresh absorbent every time. I've seen pieces of stone poulticed 6 times and more to get a stain out.
Xylene (xylol) is a good solvent to try, it's good at dissolving a wide range of oils and greases. Mineral spirits is also a good choice. These solvents don't flash off (vaporize) nearly as fast as something like naphtha or lacquer thinner, and they usually won't eat the plastic.
Remember, poulticing a small area in something like a slab is akin to creating a stain by removing a stain. The poulticed area will often be considerably cleaner than the surrounding area.