When you first Come here it is pretty simple to see the way out. But if you want to go to the last 2 Unown Puzzles follow the Green Lines on the Maps and If you want to Find Lapras Follow the Yellow Lines.
Inside Union Cave you can find TM 39, Swift. It's on the Lower Level of Union Cave. You don't need Surf, Cut, or any other HM to get to it.
Lapras
To Get Lapras, It has to be on Friday, Follow the Yellow Lines on the map (Or Keep on Going South in the Cave)