There are a bunch of factors that go into choosing the right running shoe, including what kind of surface you run on and if you have a high or flat arch. This infographic from REI summarizes all the basics of running shoes, including tips for when to replace them and how to lace them.
The graphic, for example, suggests you choose shoes with more cushioning and flexibility if your ankles tend to roll out (underpronate) or ones with motion control and extra stability if your ankles roll in (overpronate). How to tell? One clue may be the height of your arches: High angles probably underpronate, while runners with flat feet normally overpronate.
Another tip is to estimate about how many miles you run and how fast, so you can figure out if it's time for new shoes. (The average shoe lasts between 300 and 500 miles, according to the graphic, but if you run very fast shoes will get extra wear and tear.)
There's also a handy guide to lacing shoes to alleviate foot problems (a topic we've mentioned before, but now summed up here graphically).
Here's the whole infographic with all the shoe tips (click to expand or right click to save):
Of course, getting fitted for shoes is best if you're a serious runner, and there are other tools like the previously mentioned Runner's World Shoe Finder, but it's still good to know the basic running shoe info here and what your running style is like.
Running Style and Your Shoes [infographic] | REI via Daily Infographic