If you take over from another person, they have to give you their logon and password and registrar's URL. Logon and change the password so that you now have ownership of the domain name.
Next go to an area called "Manage Contacts" or something like this depending upon your registrar. This area will have a registrant, technical contact, administrative contact and billing contact area.
You usually only need to fill out the registrant contact area and then check a box to make the info the same for the other areas as well.
You will probably want to put in a new email address so that you will receive the confirmation email for this change.
Save your changes.