I keep running into this situation in my games because I like playing the 3-4 opening in most games. 
They’ll attach at 3-3 and I’m not sure how to prevent it from turning into a mess. I feel like I should be able to press on the invasion and kill it, but it gets complicated fast.
Can anyone help me?
Hane, pray that they cross-cut, then extend. The way God intended.
Here’s an example that just came up. Would anyone be willing to walk me through it?
I assume you are referring to the bottom-left corner since you killed the top-left invasion.
I added a couple of variations to the game page. Other players may be able to add more.
As a more general principle. If you are having difficulty responding to a particular move, use it against stronger players in games and see what they do in response.
[edit] ignore my variations. Smurph has done it much better (and right). The snapback in his simple variation is nice.
I added my 2 cents.
Thanks everyone! 
Gives me some things to think about…