What steps should I take to start her process before I turn 21?

If your mother entered without a visa, your 21st birthday will not magically solve the problem of her immigration status. In special circumstances, the government can make an exception and forgive an illegal entry and an illegal presence in the U.S. and grant a green card to a relative of a U.S. citizen or permanent resident. But that's an exception, not the rule, and you should talk to an immigration attorney to see whether your mother's case might have such special circumstances. Try to find a good specialist. If your friends cannot recommend one, call American Immigration Lawyers Association for a referral.