You have plenty of examples contributed by the community, easily browseable here:
http://angular-ui.github.io/ui-leaflet/examples/0000-viewer.html#/basic/tiles-example.
Let's see some progressive examples showing how to use the library on your AngularJS code. Before continue, we must have some notions of how to initialize an AngularJS app. You can find more information about a basic setup of an AngularJS application on the official AngularJS page.