What should I do if I am a resident of the US and would like to bring my mother here from Mexico?

It is currently taking about 2-3 years for a parent of a green card holder to get an immigrant visa. For Mexico, it is a longer process.

As a green card holder, there is no provision under the law for you to file any petition for your mother. A green card holder, (unlike a US citizen can file petition only for your spouse and or children) Once you however file and become a US citizen, you may then file petition for your mother. Such petition is adjudicated very quickly and as an immediate relative of a US citizen, visa is immediately available for her. Assuming your case is properly done by an experienced immigration attorney, your mother can come to the US within one year.

You will need to wait until you become a naturalized US citizen in order to sponsor your mother for lawful permanent resident status in the US.

To petition the government for your mother's immigrant visa, you have to become a U.S. citizen, first. From the day you file papers for her, the process will take about a year. To avoid any delays, make sure to file for your naturalization 3 months before the 5th anniversary of your green card (3rd anniversary if you received your green card through a marriage to a U.S. citizen), file your tax returns, and show on your tax returns enough income to qualify for sponsoring your mother (at least $19000 a year if you live alone, over $24000 - if you have one dependent on your taxes, over $29000 - if you have 2 dependents, and so on).

If you are a US citizen you may file a petition for your parent as an immediate relative. The petition may be filed as soon as you have US citizenship. If I can be of further assistance please let me know.

You cannot petition for your mother until you become a citizen. Maybe she can get a visitor's visa (B2) to visit you.