To see what your site will look like on a mobile device, simply click on the Mobile button in the LiveEdit toolbar.

LiveEditBar_MMobile

How can I choose whether tablet computers will see the full or mobile version of my website?

Tablet users will by default see the full, non-mobile version of your site. To affect this setting, visit the Account Info area within Aurora. (From the LiveEdit toolbar select More > Account Info.) On the Account Info tab, choose "Mobile" next to the "Tablet As:" selection. Don't forget to select the Update button to save your changes!