General information about transportation from LAX and the Long Beach and Orange Count airports is available here. See below for more specifics.
From the Long Beach Airport
The Long Beach Airport, voted one of the 10 best small airports by Conde Nast Traveler, is just 7 miles from downtown Long Beach and the Convention Center, a great option for those who can, and want to, avoid the traffic at LAX.
Additional ground transportation details about car rentals, shuttles, ride sharing and taxi information.
From LAX
LAX is around 20 miles from Long Beach (405 south), with six ways to get from LAX to downtown Long Beach.
From John Wayne Airport (Orange County)
John Wayne Airport (also called SNA) is about 30 miles from Long Beach (405 north, then take 710 south to downtown), with seven ways to get from OC to downtown Long Beach.