Walking is best. I even walk from T1 to T7/8 to catch hotel or parking or rentacar shuttles if they aren't already sitting and waiting for me at T1 (i.e. say if one has just left, you can walk to T7/8 faster than the shuttle can drive).

Re the link CalItalian already provided...
http://www.airport-la.com/info/terminal_map.html
...the overhead walkway from garage to T7/8 has its own security line. Even if you don't use the walkway, look for an escalator underneath it (just barely outside the building), take it, and you can use that security line. Good luck!