How do I make sure that a contact does not receive my newsletters?

Go to the client's subscription settings in Contacts menu > Contact name > link 'Edit info' in the top right corner > in the 'Edit Personal Information' pop-up window scroll down to the section 'Subscription Settings' > uncheck the box in front of 'Newsletters' and save the change. The client will no longer receive the newsletter even if s/he is the groups selected when sending the newsletters.

For unsubscribing contacts in bulk, you can use the Search Contacts tool. A tutorial:

How to do an advanced contact search, select multiple contacts and apply an action