Either drive down I-35 or fly in. The airport is new and compact. A car isn't that necessary for a tourist if you stay downtown. If leaving by car, try to do it before noon so you don't get caught in a big line of semis at the Border Patrol checkpoint.
Traffic is horrible for this small a city. Too many semis, uninsured drivers, and Mexican drivers who are used to ignoring stop signs, etc.... Consider yourself warned!
Getting around Laredo without a car is a pain in the .... but the buses exist to get you to major destinations. Taxis are tremendously over-priced and charge even more for crossing you across any international bridge - you are better off getting a ride to bridge 1, crossing by foot, and finding another ride in Nuevo Laredo, Mexico (if you were planning on going to Mexico). The bus schedule seems to always be behind but all the more reason to be on time since the bus leaves almost as soon as it gets there if it is running late. All bus routes loop back to the Jarvis Plaza/Greyhound station area so getting from the one side of town to the other involves a trip downtown. Public transportation is not very well developed but if you are just here to visit Mexico or do business downtown, then walking is the way to go.