If you're only referring to Frontlines then when you have duty finder up, click the cog at the top (on the left?) and select the freelancer option and it'll queue you up and temporarily align you with another GC if needed so your queue is (hopefully) shorter.

If you actually want to change your Grand Company though, go and talk to the administrator (2nd NPC from the left?) behind the desk at the GC you want to join. The first change is free, subsequent ones cost 50,000 gil and you can't change back within 30 days (I think that's right, might have changed).

However, you will start at the lowest rank of the GC (unless you previously levelled it/changed) and if you have a squadron it'll still be there, but you'll have to get up to the relevant rank again to actually access it. You also won't be able to use any GC specific gear if you have any.