How to checkout to a remote branch that someone else is working on in git?

First, fetch all branches from remote:

git fetch --all

Say you want to checkout to production from the remote.

git checkout --track origin/production
# Branch production set up to track remote branch production from origin.
# Switched to a new branch 'production'

(--track is shorthand for git checkout -b [branch] [remotename]/[branch])

This will give you a local copy of the branch production, and any update that has been pushed will also show up remotely