I believe that there is some convoluted way to get your eligibility by being an extra and collecting enough vouchers or something. Usually, one obtains eligibility by auditioning for and getting a speaking role or "day player" part, but you have to have a talent agent in order to line up the audition with a casting director. Once you've completed the shoot, SAG will send you a packet informing you that you are eligible, but the dues that you must pay to get your "card" are pretty steep. All this varies from state to state; I hear it's hard to get in the door in Cali for any serious auditions without your eligibility.
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"just a sack with a hole in it that cums" (Blue qtd. in Jordan).