What is the process for getting papers for my husband?

Under the current immigration laws, he is not eligible to legalize his status within the US if he entered the US unlawfully. He would have to go back to his home country but as soon as he leaves the US, he will trigger an automatic 10 year bar to reentry, which can only be waived by a showing of extreme hardship to a US citizen spouse, which is fairly difficult to do in most cases.

It depends on the particulars of his situation. But at a minimum, you will need to submit an I-130 relative petition on his behalf with USCIS to get the process started.

There is a lot of information that is required in order to give you an accurate answer. I could assume that since you are 18 that your husband is close to your age and he may qualify for DACA. You could also qualify for a provisional waiver depending if you are a U.S. citizen, but in order to advise you would need to provide more information. Get in contact with an experienced immigration attorney and they will be able to tell you how to proceed.