You have to be a United States Citizen to become a SEAL. No exceptions.
Once you've seen a Navy recruiter and passed eligibility tests you will be referred to your local Special Warfare/Special Operations Mentor or coordinator for a Physical Screening Test.
Once you've passed the PST, your recruiter, Special Warfare/Special Operations Mentor or coordinator will request a reclassification for you into the SEAL program. The reclassification will generate a SEAL contract. The SEAL contract will supersede the Navy contract you originally received.
Stay fit because you'll need to pass another official PST 14 days before boot camp. Fail the PST and your dreams of being a SEAL will be over.