How do I bring this face up and snap to another face? How do I move this selected faces up along the Z axis and snap it to the unselected faces? They were originally connected together, but I cut them out initially thinking I didn't need them. The vertices that are supposed to be connected together are on the same Z axis. I tried different settings in snapping but the selected faces seem to just jump all over the place. I need to keep the sizes of the selected faces the same, so I can't just select vertices and snap them up. I need to move everything up together.

Thank you.
What I use is the Bridge Edge Loops function. It's not perfect since it won't move all the faces but will connect the top edges cleanly.

Make sure you are either in Edge or Vertex Mode and select the two Edge loops you want to connect.



Press W and select Bridge Edge Loops.



In the operation settings, check Merge and set Merge Factor to 0. If 0 moves the wrong  Edge loop then set the value to 1.





Lastly you'll have to move the rest of the faces manually. It's not perfect but works well enough for my own usage. I believe this is what user277143 is referring to but as I can't add comments yet I instead created a new answer.