So this is probably an obvious question, but I thought I'd ask anyway.
As everyone knows, Cresselia is a huge pain. If I'm only running one counter to Cresselia (such as Tyranitar), will I be fine? Otherwise, if I'm not running a Taunt user, is the best way to handle Cresselia just to target its partners then gang up on it 2v1?
The best way to handle Cresselia (or any Pokemon in VGC) is to make it dead weight on the field. For a support mon like Cresselia, this is an easier task than most offensive juggernauts.
The simplest option is Taunt, as most won't have Mental Herb except for Trick Room. Cresselia isn't particularly fast, so you generally won't even need Prankster to get it off first. However, most Pokemon don't have the room for Taunt, so you'll generally look towards other options.
Because Cresselia often uses Thunder Wave or Icy Wind for speed control, Substitute is a great way of penalizing a Cresselia user. If you can get a Substitute user who can stay safe from Cresselia's partner, or else get a sub up on a Protect, you'll be ahead of the game. Someone mentioned Sub Latios above, which works if Cresselia is weakened somewhat, but Sub Latios on its own will be forced to switch if it tries to take down Cresselia with no help.
Finally, as others mentioned, there are a handful of attacks that can OHKO Cresselia, but while they are simple, using the mons involved may not be the easiest for a beginner. Use these if you really need to, although keep in mind that attacks that hit this hard don't limit their usefulness to Cresselia.