It depends on the live wallpaper in question, but in general, the wallpaper only runs when the home screen is visible. Since you're usually running an app or have the screen off, the live wallpaper has no effect most of the time: the extra battery use is limited to when you're looking at the home screen.
This isn't always true, though. Some live wallpapers also run extra things. For example, the live wallpaper might periodically run in the background so that it can change its appearance based on your email inbox, or weather reports from the internet, or the accelerometer. For that reason, some live wallpapers might use quite a lot of battery.
In that respect, live wallpapers are no different from any other app. If they're inefficient or do a lot of work, they'll run your battery down quickly. If they're efficient and simple, you won't notice any extra battery use. Unless reviewers comment on it, you won't know until you try.