Depending on how many remotes are present for your local repo, follow the appropriate flow.

Checkout a remote branch workflow:

For repos with one remote:

If your local repo is having just one remote for example just origin:

git remote -v
origin  https://github.com/my_username/AwesomeRepo.git (fetch)
origin  https://github.com/my_username/AwesomeRepo.git (push)

Then you can simply do:
git fetch
git checkout some_branch_name

For repos with multiple remote:

If your local repo is having multiple remotes:

git remote -v
origin      https://github.com/raisedadead/wiki.git (fetch)
origin      https://github.com/raisedadead/wiki.git (push)
upstream    https://github.com/FreeCodeCamp/wiki.git (fetch)
upstream    https://github.com/FreeCodeCamp/wiki.git (push)

Then you have to specify a remote as well:
git fetch
git checkout -b some_branch_name <remote>/some_branch_name

where <remote> in this example is either upstream or origin.