To find out what an app does with your information (your name, your measurements, your habits), read its privacy section on the store listing before installing it.
Open the app store (App Store on iPhone, Google Play on Android), tap the magnifying glass, type the name of the app, then tap its name. You should see its listing: the page that presents the app, with the Get or Install button.
On the listing, scroll down to App Privacy (iPhone) or Data safety (Android). You should see the list of information collected, and whether it is shared.
After installing, open Settings > Privacy & Security (iPhone), or Settings > Apps > the name of the app > Permissions (Android).
Refuse the permissions the app does not need: a sleep app has no need of your contacts.
If you don’t see it: a listing with no privacy section, or marked « No details provided », is a warning sign. Read the publisher’s privacy policy instead: look there for the passages on sharing, selling, retention periods and deletion of your information.
Limitation: the store listing is filled in by the publisher itself. The store does not always check it.
To picture it: giving information to an app is like lending out a notebook. You need to know who will read it.