Having lived a good portion of my life in San Antonio, I've pretty much figured out how to get around town without getting myself lost, but I've heard newcomers and visitors say it can be quite difficult to figure out where they're going. Admittedly, the street layout can be confusing (what with dead ends and streets starting and stopping and other such peculiarities), but the highway system was planned out very well, and it's pretty easy to figure out.
Three interstate highways, a couple of U.S. highways, and some state roads make up the backbone of San Antonio's road network in a classic hub-and-spoke pattern focused on downtown. The city is also encircled by two concentric loop highways that make navigation as easy as saying "inside" or "outside" the loop. In fact, if lost in the Alamo City, you could always just head in one direction until you hit 410 (the inner loop) or 1604 (the outer loop) and just follow it around until something looks familiar. This could take some time, though.
(For another San Antonian's complete treatment, check out the Web site of the Texas Highwayman. He's really into highways.)
But, one important thing to remember is that street names in San Antonio can be strange. And, by all means, if you are getting directions from somebody, copy down the street names carefully. That's because there are a number of streets that share part or all of their names with others, and these streets are usually in different parts of town.
Some examples off the top of my head:
1. Wurzbach Road and Harry Wurzbach Road
2. Perrin-Beitel Road and Naco-Perrin Boulevard
3. Vance Jackson Road and Jackson-Keller Road
4. Guilbeau Road, New Guilbeau Road, and Old Guilbeau Street
5. Callaghan Road and Callaghan Avenue
6. Southeast/west Military Drive and Northwest Military Highway
And others. Just make sure you have the right street name. And, if possible, use a map.
By the way, if someone tells you to take a highway and they use a person's name to describe it (such as McDermott Freeway, Connally Loop, Stotzer Freeway, etc.), they're new to town. Long-time locals still call the highways by their number names (IH-10, Loop 410, Highway 151, and so on), and they probably will for some time now.