Well, first you have to check if first cousins are allowed to marry. You can take a look at this link: http://marriage.about.com/cs/marriagelicenses/a/cousin.htm
It looks like it is recognized. Then you still have to get by the belief that USCIS will just think that you married to get the green card
. So you will have a tough fight ahead of you. Your best bet is to have an attorney which you can find at http://www.ailalawyer.com/
After you marry, you file the following: I-130 (Petition for family member), I-485 (application for Lawful Permanent Residency), I-765 (Application for work permit), G-325a (Biographic data - one for each of you), I-693 (Medical exam that a certified doctor must fill out for you), 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, marriage certificate, divorce certificates if either of you have been married previously, 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, she should get a work permit. About 5 to 7 months after filing you should get a marriage interview. If all goes well, a few weeks later she should get a Residency status (green card).
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