There are 2 ways to remove someone from a campaign: either by starting from their Account page, or while viewing the Campaign you want to remove them from.
Method 1: From The Account:
Go to the Accounts tab, search for the Account you want removed from a campaign, and click it.
While viewing the client's account, simply click the 'Campaigns' tab across the top of the account screen and remove them from any campaign by clicking on the unsubscribe icon (looks like a "minus person" image):
Method 2: From The Campaign:
If you are already working inside of a campaign - you can open up the subscriber list by clicking the "View Audience" button:
From there you will see a list of subscribers and you can simply click on the unsubscribe icon (looks like a "minus person" image) to unsubscribe members from the campaign.
Please note - this will only remove clients from a specific campaigns and not 'Opt Out' a client from all future communications from the system. If you are looking to 'Opt Out' or 'Unsubscribe' a client from ALL future messages you will want to follow these instructions here.