Wait for your turn in the line on the right.
Go inside the hut and choose "I want to dig!" after talking to the guy at the counter.
The guards at the temple will let you in now.
Inside the temple, Gippal will ask you to follow him and you'll get an Al Bhed Primer.
Go out and south until you run into Gippal again.
Answer "We're sure." when he interviews you and he'll give you the Letter of Introduction.