If you and your husband qualify, the major forms needed for adjustment of status are the Form I-130 (petition for alien relative) and Form I-485 (application for adjustment of status). The forms and instructions are free at www.uscis.gov . Other forms would also need to be submitted.
Before filing anything with USCIS, both of you should check with an attorney to see whether both of you qualify.
There are many reasons why one or both of you may not qualify.
Given the lack of information in your post, it likely would be better for you to consult an attorney. If your husband does not qualify for adjustment of status and is in the US illegally, filing an application with USCIS may trigger a deportation proceeding against him.
First, you state that your husband is already in the U.S. Immigration laws require entry pursuant to a valid visa or via a Visa Waiver country to have the potential to adjust if marrying a U.S. citizen (which you do not state that you are... ) If your husband entered illegally (EWI) entry without inspection, he will be called to his embassy for consular processing, and you will be required to file a waiver. If he has been deported/removed previously, and/or has stayed in the U.S. for a certain length of time, has worked without authorization, has committed any crimes, then you are looking at a situation with complications, and even 10 year or permanent bars to residing in the U.S. Also, some situations, depending on the entry, lead to a question of immigrant intent, and if that is found to be present, that can also complicate your case and lead to a denial of adjustment of status.
That said, the basic "forms" would be I-130, I-485, G-325A, I-864 (Affidavit of Support), I-765(work), I-131 (advance parole for travel while adjusting-- and here the intending immigrant if in overstay should NOT leave the U.S. or he would be facing the trigger of unlawful presence, and a 3/10 year bar from re-entry. Past deportations can mean a permanent bar to reentry-- so if any order of removal or actual removal/deportation or appearance in the Immigration Court... then you should NOT PROCEED without a thorough consultation with an experience immigration attorney... as the very act of trying to adjust by the rules, (if you previously broke the rules), can lead to a NTA (Notice to Appear),
Removal, and the opposite, in short of your being able to petition for your husband "already in the U.S."
If your husband entered validly, such as on a student visa, even if it has expired, if you are a US citizen, and there are no other immigration violations, then you face a potentially easier time adjusting. (There are Waiver forms to request "forgiveness" for some rules that have been broken). If he's on a valid visa, such as an L, then
you face an easier scenario. No travel outside the US should be done (form 131 advance parole) during the adjustment, unless the husband (beneficiary) has held a valid status including through the time of your
filing for him.
Other documents you will be gathering for this process, include but are not limited to: Birth Certificates, Divorce and or Death Certificates if any of a prior marriage are applicable, Marriage Certificate, Any Children Born-- their birth certificates, applicable size and view photos, three years of tax records and salary & assets (for the affidavit of support), and relevant correspondence and photos in support of your "bona fide" valid marriage.
There's your homework! If you state your citizenship or immigration status such as lawful permanent resident (green card holder), and your husband's status, and if any prior marriages/divorces, and children, type of visa if any, if the husband/spouse has been here in overstay, illegal entry, deported/removed and these type of facts, this really helps (us) immigration attorneys to offer you more useful advice.
There are several ways for an individual to be sponsored for immigration purposes. It could be through a family relationship or through employment. If you are a U.S. Citizen spouse filing for a foreign national then you would want to file an I-130 and (if your spouse entered the U.S. with inspection) you can also file (simultaneously) the I-485 Adjustment Application. These documents are filed with the NBC. Your question is somewhat vague however and we do recommend that you see proper Legal Counsel before you proceed.