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If you are a U.S. Citizen and he is under 21 and single and he entered the U.S. legally on a visa that allows adjustment of status, then you can file the following forms for him to stay: I-130 (Petition for family member), I-485 (application for Lawful Permanent Residency), I-765 (Application for work permit), I-131 (Application for Advance Parole), G-325a (Biographic data - one for each of you), I-693 (Medical exam that a certified doctor must fill out), and 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/forms.
The supporting evidence that you would file would be birth certificates, proof of your U.S. Citizenship, proof of your spouse's legal entry into the U.S., and financial documents to prove your income over the last year at least.
In about 3 to 5 months after filing, he should get a work permit and Advance Parole. About 5 to 7 months after filing you should get an interview (though now it is taking longer, so maybe closer to 7 to 9 months). If all goes well, a few weeks later he should get a Residency status (green card).
If he is older than 21 or you are not a U.S. Citizen, then all you can do is file an I-130 for him and it may take awhile before he is able to immigrate to the U.S. Here is a link:
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