Providing your boyfriend has a visa, and was inspected at port of entry, you can adjust status once you are married, all you need to do is go to the USCIS website, and download the following forms.

I-130, I-485, I-765, I-693, I-864

You need to be earning around $17500 to be your boyfriends sponsor, if not you will need to find a co sponsor (maybe a family member or friend)

AOS application is costing $1010 plus the fee for the I-130

I hope this helps