Identify where you want to live in Mexico. Your choices are many: beaches, mountains or deserts. Prices of homes vary by location, with beach front properties leading the high-end homes, and desert homes being the least expensive.
Contact a real estate agent who is a member of AMPI. Real estate agents do not have to be licensed in Mexico, but using one who is an AMPI agent (Associan Mexicano Professional Imobilarios) is a good idea, because they follow a code of conduct and are a self-policing organization. While not the norm, there are unscrupulous people everywhere.
Meet with your agent, find out who he uses as a real estate attorney, and let the agent know what exactly you are looking for in a house in Mexico.
Meet with a mortgage banker if you need a loan. Fill out the paperwork and see how much you will qualify for based on your income and net worth.
Select a home from the ones you have looked at, meet with the attorney and have the home inspected.
Sign the paperwork once the home has been inspected, the title cleared and the lawyer says that things are completely legal.
Go to the closing, finish signing the paperwork and accept the keys to your house in Mexico.