Android Pay should be rolling soon, but if you can't wait for "soon", there are ways to get the app working on your phone now. Well, kind of...
Google Play Services 8.1 has already started to appear on some handsets, which makes sense because that update is necessary to run Android Pay when the official launch does eventually go live. If you're one of the few who already has the updated Google Play Services on your phone, there's apparently an activity hidden in the app for the new Android Pay system.
While an activity isn't actually an app (it's just the starting point for an app) there are ways to get it up and running as if it were an app.
All you really have to do to get the activity running is install an activity launcher on your phone and use it to launch the Android Pay activity from within the Google Play Services app. It's not guaranteed to work, though, and since Android Pay's not live yet, there's a chance your info might not be completely secure if you choose to try it out.