I don't see a direct link on the User/Patron account page to be able to check out an item. It seems that you have to go back to the main menu and select "Manage Patron Services". In Voyager, you can easily get to the Charge window from the Patron window or vice versa.
There is the "Manage Fulfillment Activities" link. I think it would be helpful if you could add the Check-out function on that page.