[git] Update a local branch with the changes from a tracked remote branch

I have a local branch named 'my_local_branch', which tracks a remote branch origin/my_remote_branch.

Now, the remote branch has been updated, and I am on the 'my_local_branch' and want to pull in those changes. Should I just do:

git pull origin my_remote_branch:my_local_branch

Is this the correct way?

You don't use the : syntax - pull always modifies the currently checked-out branch. Thus:

git pull origin my_remote_branch

while you have my_local_branch checked out will do what you want.

Since you already have the tracking branch set, you don't even need to specify - you could just do...

git pull

while you have my_local_branch checked out, and it will update from the tracked branch.