Be polite and professional. Introduce yourself and tell them you'll be moving from a great distance. If this is a place you'd like to be considered for, ask if there is a waiting list for vacancies. Then, you'll need to visit and start viewing places. Unless the market is unusually tight, I'd recommend you do this around the first of the month in the month prior to when you'll be moving.
People usually give notice around the first.
So, if you're looking at moving July 1st, I'd be in Los Angeles on or around June 1st to make as many viewings as possible. This will give you maximum exposure to available rentals. The next step is to sign the lease and plot the move - I'll leave those two steps in your capable hands. Top of page Disclaimer Information provided by Greg should not be construed as real estate or legal advice. State and local laws may vary, so please consult legal counsel in your area with respect to your individual situation.