What form do I need to fill out if I am twenty-one years old and would like to start the process to legalize my mother?

Where is your mother? Is she in the US? If so, did she enter the US lawfully or unlawfully? Are you a US citizen?

If your mother - came to the U.S. legally and was inspected at the border and granted admission; - was not convicted of any crimes; - was never involved with a totalitarian party or a terrorist organization; and - is not disqualified from becoming a permanent resident of the U.S. for some other reason; then you file forms I-130, G-325, I-864, I-485, I-765, and I-131 and wait for your mom to get a green card interview. (If your own income is not enough for Form I-864 Affidavit of Support, you will have to find a co-sponsor for your mother; the co-sponsor must be a U.S. citizen or have a green card and must make enough money to be able to guarantee that your mother will not become "public burden" (receive food stamps, SSI, Medicaid, subsidized housing, etc.)) If your mother came to the U.S. illegally, don't waste your money on the filing fees: you cannot legalize your mother. There are some rare exceptions, and you might want to talk to an immigration attorney to see if one of these exceptions can help your mother. If your mother was ever deported?, or was ever convicted of a crime (not all criminal convictions are a problem, but most are), or has a contagious disease, or was ever involved in a terrorist organization or a totalitarian party, talk to an immigration attorney to see whether there is something that can be done to overcome these barriers to your mother's legalization. Most immigration attorneys work to earn a living, so a consultation will cost you some money. But it will be a smaller sum than the $1500 you would send to the government with the applications that have no chance of being approved.