If you want to create a branch from the current branch
git checkout -b {your_local_branch_name}
you want a branch from a remote branch, you can try
git checkout -b {your_local_branch_name} origin/<remote_branch_name>
If you are done with changes you can add the file.
git add -A or git add <each_file_names>
Then do a commit locally
git commit -m 'your commit message'
When you want to push to remote repo
git push -u origin <your_local_branch_name>
All together will be
git checkout -b bug_fixes
or If you want to create a branch from a remote branch say development
git checkout -b bug_fixes origin/development
You can push to the branch to remote repo by
git push -u origin bug_fixes
Anytime you want to update your branch from any other branch say master.
git pull origin master
.