How can I help my deported boyfriend who entered the US illegally?

Question is too vague.

Schedule an appointment with a competent attorney who can explain options available. Truth is that the requirement may be that your boyfriend return back to his native country before he can obtain legal status in the US. As a general proposition it is very difficult to obtain legalization in the US if the applicant for immigration benefits arrived in the US without permission to do so. Not entirely impossible, just generally really difficult. So rather than bore you with the options that may be there and instead of pursuing through senseless pages of Internet garbage that explain nothing, I would schedule some time to speak to someone who knows and can explain the deal before you. No process like this is easy, but you will be very well served by finding an attorney who will not BS you and will level with you and your boyfriend as to the real options available. Good luck.

That is a very serious problem, since it's a felony to illegally reenter after deportation. If you're married, you can begin filing documents but it is a long process with many potential problems, not least of which that he's under a bar to reenter legally.

Your question requires an attorney consultation. It is not a simple question that can be answered on this type of forum. There are many factors that would need to be considered and evaluated, such as when and why he was deported to begin with and whether he is subject to a 10-year ban. I strongly suggest that you contact an experienced immigration attorney for a face-to-face consultation and give him/her all of the facts surrounding your boyfriend situation. He/she would then be in a better position to analyze his case and advise you of his options.