If you're brand new to Lightning on the Salesforce1 Platform, and you're having a bit of trouble following the cool but relatively complex Expenses sample app from the Lightning Components Developer's Guide, maybe this Lightning-to-Lead tutorial will work better for you.
The goal is simple: Create a one-page app that basically does what Web-to-Lead does, which is to create a new Lead record. Nothing glorious, but it's just complicated enough to go over some core concepts. When you're done, you'll end up with a simple page with a few fields and a lone button.
Sound simple? Give it a try and let me know what you think!