What is the best way to add a contact to existing membership using relationships?
From your description it sounds like you want to have a membership type that applies to a household and which subsequently applies to any individual with a given relationship to that household (probably the "Household Member is" relationship).

To make this work it needs to be set up before you have any memberships in your database. As soon as one of these memberships is applied to a contact, you can't then change the relationship element of the membership type.

From your question it sounds like this is where you are: you've created the membership type but not set the relationship, and then you have created a membership for one or more contacts and so can't now edit the relationship settings for the membership type.

How to get round this? One option that might be workable subject to the volume of memberships that you might need to edit could be as follows:

Create a new membership type that matches the settings of your current membership type, but add in to it the required relationship setting.

Then you could go through each of your contacts that has one of the original memberships, and edit it to remove the original membership and add the new membership (the one with the relationship setting in place).

Then any related contacts would automatically have the membership applied via that relationship. As I say this approach could be workable if you don't have too many records with the old membership, otherwise it might not be a sensible manual task, and an alternative approach, such as manipulating the database directly, or via the aPI, might be more suitable.

To add a relationship setting to your membership type, you need to decide which relationship is the right one. This is not necessarily intuitive, but depending on the version of CiviCRM you are running, there may be a useful pop-up help window when you click the question mark icon. 

It reads: 

"Use this field to configure Membership Types where memberships are automatically granted to related contacts. Examples:

Relationship Type: 'Household Member is'

Direct member is: a household

Membership is automatically granted to: 'Household Members' of that household"

I think that might fit your particular requirement. If required you can also optionally set a maximum to the number of these related memberships that are allowed. For a household this might not be particularly relevant, but is often useful when the direct member is an organisation.