Way I tend to create a topic branch in git-scm for a specific issue:

git checkout -b  # create a local branch
# Do some stuff. We decide that its worth pursuing, so lets add the branch to the remote repo
git push origin [branch-name] # push the local branch to the remote repo
git branch --set-upstream [branch-name] origin/[branch-name] # make branch track remote
# Carry on working in the branch