Before it can be used, polymer clay must be conditioned to soften it and strengthen the finished product. There is some difference of opinion on how much conditioning is necessary, but the general rule of thumb is that you should condition clay until it is workable.
If you can roll the clay into a snake and fold it in half with no "cracking" in the snake, it should be fine. Or, if you are mixing two or more colors of clay, by the time the colors have merged, the clay should be thoroughly conditioned.
Some brands of polymer clay are firmer than others. Similarly, older clay may require more conditioning than fresh clay. Workability can also vary between batches of the same brand of clay. These days, many brands of polymer clay are fairly malleable right out of the package. It is still generally recommended that you condition these, but they will require much less work than very firm clay.
Condition soft clay by kneading, scrunching, rolling, and folding it repeatedly. Feed it through a pasta machine repeatedly to save your hands some work. You may find it helpful to gently warm tougher clay or clay that you have just taken out of cold storage. (Do this by sitting on it, putting it in your pockets, etc. Just be sure that it doesn't get too warm, as this can ruin the clay by partially curing it. Never place uncured clay in direct sunlight.) Though it is not often necessary with most clay brands, some clay may be so hard that you need to use a food processor to soften it.
Some brands of clay-or old clay-or sometimes just unfortunate batches of a brand of clay that is usually soft-may be crumbly. Though you may be able to condition crumbly clay without additives, crumbles often mean that the clay needs more plasticizer. Soften crumbly or very hard clay with Mix Quick (from Eberhard-Faber), Sculpey Diluent (Clay Softener), mineral oil, or petroleum jelly. Start with a very small bit of additive and continue to mix in small increments until the clay is workable. If you have translucent clay in a softer brand, you can also mix this into the firmer clay. Be aware, however, that if you add a very great deal of translucent clay, it will change the color of the other clay.
If you accidentally add too much softener to the clay, or if the clay is softer than you like it right out of the package, you can remove some of the plasticizer by leaching it. Leach clay by placing it between sheets of blank paper. (Inks on papers can transfer to clay, so avoid marked paper.) Some people like to speed up the process by weighing the paper and clay with a heavy object, such as a book. (Just be sure to put a sheet of plastic wrap or other barrier between the leaching paper and the weight, if you don't want plasticizer leaching right on to the next layer!) Check the paper after a little while. The oily residue on the paper is plasticizer. Test the clay once you see this residue. If you find that the clay is still too soft, you can leach it some more. (You may wish to replace the paper with a fresh sheet, if it's very oily.) If you over-leach the clay, you can always resort to an additive. Just mix in a drop at a time.