These are some of the guidelines to verify the correctness of the SDK integration.
The most important thing is to ensure that the app is working as it was before integrating with the SDK.
There are 4 components to verifying the integration:
SDK initialized correctly
Make certain events are being fired, ie that identify, click, app_open etc., are being fired correctly from the app.
Confirm that the events show up correctly in the Dashboard, under the user profile
Use the Push Studio editor to create different types of push messages and ensure that the notifications render correctly on devices.
Create a test campaign with the test devices and run a campaign against them, making sure that you are getting stats. Please note: iOS doesn't give any delivered stats.