When posting such questions you should give the terminals listed in your itinerary. LAX terminals are more divided by airline (there can be more than one airline in a terminal) than by domestic vs. international per se. The Tom Bradley Terminal is all interantional but you shouldn't have to deal with that. Look at a terminal map such as www.airport-la.com/info/terminal_map.html (click on each number) I assume your Delta flights will use Terminal 5 and your UA flights 6-8 (connected). Arriving you will, of course, go through Immigration and Customs, but, assuming your bags are tagged for LAS, should be able to hand off your checked bags at a transit desk outside Customs. You could take the free shuttle counter-clockwise from UA to DL but I'd probably just walk (exit and go to your left; I think it's easiest down at the arrivals level). On the return, the shuttle would be going in the same direction as you'd walk but, again, I'd probably just walk.
Do confirm that your bags each direction will be transferred between the two airlines. I think they will be, but you might watnto phone to make sure (you don't want to walk on to the next terminal without your checked bags and find they weren't transferred; more of a chance for this on LAS-LAX-Oz, since on the arrival you'll have your bags in your hands after you you leave the baggage carousel after Immigration and before Customs).
Edited: 8:23 am, December 04, 2012