First, create a new local branch and verify it:
bashgit checkout -b <branch-name>
When you push it to the remote server, it automatically creates a remote branch:
bashgit push <remote-name> <branch-name>
The <remote-name> is typically origin, which is the name provided by Git for the remote server you cloned from. Then, your colleagues can simply pull the branch.
However, note that the format is:
bashgit push <remote-name> <local-branch-name>:<remote-branch-name>
When you omit one parameter, Git assumes both branch names are identical. Nevertheless, be cautious not to make the critical mistake of specifying only :<remote-branch-name> (using a colon), as this would delete the remote branch!
To inform subsequent users how to git pull, you might want to use:
bashgit push --set-upstream <remote-name> <local-branch-name>
As described below, the --set-upstream option configures the upstream branch:
For each latest or successfully pushed branch, add an upstream (tracking) reference used by
git pullwithout parameters and other commands.