The first way into SAG is achieved by obtaining three background talent vouchers. Basically, if you work three days as a SAG extra - you will then be able to join the union. Don't forget that even after you obtain these vouchers, you still have to pay the initiation fee which is over $2,000. It is much easier to obtain vouchers in Los Angeles or New York.
The second way is by landing a speaking role on an AFTRA show. AFTRA is another actor's union that governs all soap operas. If you have a speaking role on a soap, one year from the day you worked on the soap you will be eligible to join SAG. Be sure and save your employment contract from the soap opera.
The final way to get into SAG is through a Taft-Hartley which is a form that productions will fill out to basically escort you directly into SAG. In this case, if they want you bad enough a production will pay the fees associated with the Taft Hartley to get you straight into the union. This avenue into SAG is very rarely traveled by the average actor.