To make someone a member, or to remove someone from Membership, open their Person record, and click on the plus sign (+) next to "History" section.
Adding to Membership:
If they are a nonmember, and you want to make them a member, you will see a button that says "Receive as Member." If you click this option, you can then select when and how that person became a member of your church.
Removing from Membership:
If they are a member, and you want to make someone a non member, you will see a button that says "Remove from Membership." Click this button, and you can select when and how this person left membership at your church.