I found sometimes just clicking on the wormholes doesn't work as you would expect, at least not in the same way as it would if it were just a new starlane. Before the patch I could simply auto-path using it as if it were another starlane, but after the patch I found two new features (could be old though, I'm not positive):
1) In order to use them now you have to actually force the ships at the wormhole to converge at the very center of the wormhole gravity well which causes them to instantaneously appear at the other wormhole end. (You'll see the green pathing lines of the ships all converging radially toward the center point of the gravity well when you click on it). So it requires an extra step of micromanaging compared to normal starlane travel which auto-paths pretty well.
Since you are probably already familiar with micromanaging normal starlane travel, say, as when the computer auto-paths your tiny band of cobalts through a pirate base to get to a planet on the other side, forcing you quickly construct a manual path (chained shift-clicks) around the base...this should not be much of an unexpected feature.
2) Prior to the patch I never encountered a wormhole that connected different galaxies, just wormholes connecting within the same starsystem. However, that observation could just be the luck of the maps I have seen so far. Regardless, the only way you can find out where the wormhole goes is just to try it. It is not predictable (as it would be if it were simply intragalactic). Sometimes they just connect to another wormhole within a star system, and sometimes to another star system.