This happens automatically. You can use a drop down menu to insert an 'unsubscribe' link in your email - users who click this are taken to a web page that confirms their wish to opt-out and following this they'll be removed from the relevant list.
You can easily export a list of unsubscribers from dotMailer to help you manage any offline lists you have - this will export in a format you choose. As a failsafe, dotMailer won't re-upload any names that have previously unsubscribed to a list - but you should always take care to delete them from your own records should you be keeping separate information locally.
If you're a web programmer, you can use our API to unsubscribe users.
dotMailer supports CSV files. The vast majority of companies and software can therefore integrate with it.