This (pinned) discussion covers some questions regarding TestFlight testing I answered by mail or addressed in other posts - and it's open for additional questions or other contributions.
Installation
Testing an app with TestFlight is just like installing an update and using the app as you're used to. Because it is no official release the installation has to be done using Apple's "TestFlight" app - let's call it an App Store for prereleases, either individually assigned to you or publicly available via links (like StitchBuddy). Here is some information from Apple about TestFlight, although I found them quite verbose: Just install and use the app. You can even test In-App purchases, which are not charged when done with a beta version. In case anything goes wrong, you can (1.) provide feedback - through the TestFlight app (or of course directly), (2.) roll back to a previous beta version of this test, or (3.) reinstall the last official release from the App Store.
Deinstallation / End Testing
The last step should also be done when a test has ended - the beta version will expire after 90 days the lastest: This way you are sure to use the official release again, and receive future updates.
Existing Data
Installing a test version via TestFlight does not touch existing data, but is only replacing the app itself - just like any update from the App Store.
Of course beta versions are less mature, and therefore more likely to harm data by any error than any official release. But let's be honest: Data corruption could happen any day with App Store releases, too. That's why I highly recommend to always keep up-to-date backup copies of your data … better safe than sorry!