How Google Play updates itself?
When you're connected to Wi-Fi and Google Play Store is running, it will automatically download any updates for Play Store and Play Services. If you have something like a network monitor, you'll occasionally find Google Play Store occupying large bandwidth and stops after tens of MB.

Updates for Play Services will be installed immediately while updates for Play Store will be installed after you quit it (by pressing back multiple times or home). As noted by @Matthew Read, apps with system privileges do not require user intervention while installing or updating apps.