Now I find it obvious, but at first, it was not.
I am using a OpenLDAP for Linux user authentication, and I am using Web based tool for editing LDAP entries called phpLDAPadmin. I needed to add a user to a group in phpLDAPadmin, but it was not obvious to me.
Click on the group on the left part of a screen (in a tree structure) . Then, in right half, click on a Add new attribute, then select memberUid and enter some username. After you press Add or Save Changes couple of times, you will notice a new link under memberUid called (modify group members), which allows you to edit members in a more user friendly way.