IF he came in with a visa and then overstayed, you will need to file an adjustment package. This includes the following forms: I-130 (Petition for family member), I-485 (application for Lawful Permanent Residency), I-765 (Application for work permit), I-131 (Application for travel permit), G-325a (Biographic data - one for each of you), I-864 (Affidavit of support). You will need to file each form with supporting evidence and appropriate filing fees. You can find these forms at www.uscis.gov.
HOWEVER, if he entered without a visa and/or was not inspected by an immigration officer, then he will not be able to become a resident inside the U.S. (meaning that he came in illegally)
If you are a U.S. Citizen, you could get married and he could file an I-130 here in the U.S. (which will give him no legal status), but once that I-130 is approved, really the only thing he can do is leave the U.S. and apply to come back in at the U.S. Embassy/consulate in his home country as the spouse of a U.S. Citizen. At that point, they will want to deny him because he entered illegally and stayed. So he would have to apply for an I-601 waiver (forgiveness) and to get this waiver he will have to prove that you will suffer extreme hardship if he is not allowed back in to the U.S. These waivers are very difficult to get. The reason they are difficult to get is because your hardship probably will need to be more than just economic hardship or emotional separation hardship. So because they are difficult to get, no one wants to risk leaving the U.S. and getting stuck outside for 10 years if it isn't granted.
You can look at this link to get more information on I-601 waivers. It is from the U.S. Embassy in Syria, but it is a good description and the process should be similar in all U.S. Embassies.
The only other options because he hasn't been here long would be to wait for a new law that would help him (maybe next year), or apply for political asylum, but I don't think he has much of a chance coming from Honduras.