I'm trying to UV unwrap the inside of a barrel I made.
The problem is, when I select the inside of my barrel, and use the
Mesh > UV Unwrap... > Cylinder Projection, I get a weird unwrapped form. How can I solve this?
Blender's automatic UV unwrapping doesn't always work correctly. You can do it manually easily if you mark(CtrlE > Mark Seam) the top seam, the bottom seam and one seam down the middle:
Then unwrap (U > Unwrap):
Aside from the ideas above you may also try applying the Location, Rotation and Scale in Object Mode using Ctrl-A.
Not doing so will really screw up a lot of the various operations in Blender, this includes UV unwrapping.