Upvote:2
IAH has a "Skyway" train that connects all the terminals inside security. Since you are traveling on one ticket, your checked luggage (if any) will be checked all the way through to Los Angeles, and you can confirm that with the agent when you check your bags in.
You'll be able to go to your gate for the second flight without going through security again. Just check the TV monitors to find the gate number for your next flight and follow the signs to get there. To change terminals, follow the signs to "Skyway" train and ride to the correct terminal.
Do not exit the secure area and take the "subway" train instead; that one is outside security.