How to Fetch Updates From Another User's Repository

I cloned anothers remote repository and branch. Now they have made updates and I want to retrieve them.

Here is what I did previously:

git clone https://github.com/username/repository.gt
git checkout origin/branchname

I think that I need to do something like
git pull origin master
then
get pull origin branchname

But when I do
git branch -a
I no longer see a branch. So should I assume that the branch has been merged? If that is the case, should I just type

git pull origin master (to get the updates)
Thanks so much for the help, as you might tell I am new to this.