How do you change the order that users appear on the login screen?
Technically this isn't possible, since accounts are shown in alphabetical order by default and there's no option to change the sort order.

As a workaround, however, if you prefix the full name of an account with a space, it'll sort at the beginning of the list. So for example, if you want to have two accounts called "Hello" and "Test", but with "Hello" on the right, name the other account " Test" (note the space).