I'm an attorney here in Texas.
You have two options: 1) you can petition for him as your fiance, or 2) you can marry him in Mexico and petition for his green card in Mexico (so he would arrive with a green card in hand). If you petition for him as your fiance, he will have to enter the US and marry you within 90 days. Which method you choose depends on your timing issues and your particular circumstances. The waiting periods are different but depending on your situation one method might be better than the other. Either way, it is an involved case that has many parts to it.
Feel free to contact me for a consultation. A consult with an attorney is the smartest investment you can make to avoid making mistakes that could jeopardize your ability to live in the US with your boyfriend. You can contact me at www.lyttlelaw.com
and we can set up a phone consultation for you.
This answer is general in nature and does not create an attorney-client relationship. You should meet with an attorney to get accurate legal advice that is tailored to your needs.
If you plan to marry the boyfriend, bring him on a fiance visa. If successful, you have 90-days to marry & get him his permanent residence. If done propery, this process takes about 4-5 months. If you want to marry him in Mexico, you must file a relative petition (I-130). This takes longer. He might not be able to come to the US for about 18 months.