To add a new member to a community, first go to the community home page while you are logged in.
Then use the grey settings button to the left of the community title to show the pop-up.
Now use the Invite Others to Join to search for that person
Click the person you want to add, and add them to the list
Then you MUST click on the green button - "Add selected to the invite List"
Then there is ANOTHER stage, which is to actually invite the person. You can either send an invitation, or add them immediately. I usually add them immediately.