Fist I'd say that if you're a new user to Drupal, using Display Suite is really jumping into the deep end. It's a really powerful module and creating View Modes is just the tip of the iceberg of what it can do. Second, when you create a new View Mode, you're doing it for an Entity (such as Content Types, Users, Comments, File - but not so much a single node, nor a field). You can find more info on what View Modes and entities are here. You don't need Display Suite to activate other View Modes but if all you're wanting to do is create a custom view mode, the lightweight module to use for that is Entity View Mode. Lullabot does a nice job of explaining this module here.
Anyhow, modules aside, note that the controls for turning View Modes on and off are only found on the 'Default' view mode for a given content type, ie: when on the Manage Display page of whatever content type you're working with, at the top right under the main tabs, you'll see your activated view modes. If you select 'Default' then you will see the control to turn on/off other view modes.
Now, maybe you're wondering how do you see what a particular View Mode looks. To do this, you're best off using Views as it ties in nicely with View Modes.
Hope that helps.
