You need to create a local branch that tracks a remote branch. The following command will create a local branch named daves_branch, tracking the remote branch origin/daves_branch. When you push your changes the remote branch will be updated.

For most versions of git:

git checkout --track origin/daves_branch

--track is shorthand for git checkout -b [branch] [remotename]/[branch] where [remotename] is origin in this case and [branch] is twice the same, daves_branch in this case.

For git 1.5.6.5 you needed this:

git checkout --track -b daves_branch origin/daves_branch

For git 1.7.2.3 and higher this is enough (might have started earlier but this is the earliest confirmation I could find quickly):

git checkout daves_branch

Note that with recent git versions, this command will not create a local branch and will put you in a 'detached HEAD' state. If you want a local branch, use the --track option. Full details here: http://git-scm.com/book/en/v2/Git-Branching-Remote-Branches#Tracking-Branches