If you need to add, edit or delete Membership Options, you can do so under Manage Your Account —> Membership Options:
On the resulting page, you will see a grid displaying the current Membership Types within your database (a sample portion of which is provided below):
Several options are available to you when right-clicking on a Membership Type here:
Selecting Edit Membership Type will allow you to edit the Membership Type name or to change the Contact Type of the Contact or Linked Contact associated with that Membership Type.
Selecting Delete Membership Type will allow you to delete that particular Membership Type as an option from your database.
In most cases, however, you probably need to add a new Membership Type rather than editing an existing one. This can be accomplished by clicking the Add New Membership Type link in the top right corner of the grid:
You'll then see the below dialog:
Then, you can just type the new Membership Type in the appropriate box and choose the contact types for the two types of records you'd use when adding this Membership Type. Then, click Save Membership Type. As an example, if you were adding the Membership Type "Brother-in-Law," you'd set "Contact is" to Individual and "Linked Contact is" to Individual, as when utilizing this Membership Type you'd be linking two contact records with a Contact Type of Individual.