There are a two different "camps" when dealing with cocoapods and Git. Some developers check in the Pods directory and some only the Podfile and Podfile.lock. I only put the Podfile and Podfile.lock in Git.
Assuming that you have the cocoa pods gem installed already, You should be able to clone your git repo and just run pod install.
In addition to the Podfile and Podfile.lock, I check in the generated .xcworkspace file as well. I use the following entries in my .gitignore:
build/
*.pbxuser
!default.pbxuser
*.mode1v3
!default.mode1v3
*.mode2v3
!default.mode2v3
*.perspectivev3
!default.perspectivev3
xcuserdata
*.xccheckout
*.moved-aside
DerivedData
*.xcuserstate
Pods/