The first step is to get in touch with the developer and share your concern. The contact information for the app developer can be found by going to the App Store app, locating the app in question and look for either App Support or Developer Website option. Once on the developer website, you can generally find the contact information.
In your message, it helps to mention the version of iOS running on your device and your device model.
To further troubleshoot and check if the misbehavior may be happening due to other reasons, it helps to update to the latest public version of iOS. It doesn't hurt to restart the device and try again.
You can also try by reinstalling the app, toggling Internet connectivity, logging in/out of Game Center (if it's a game app) etc. to isolate the issue.
If you have a different iPhone handy, you can also try by installing the app on it to determine if the issue is device specific.
It would help to include your findings in the message that you plan to send the developer.
Some apps have built-in mechanism to automatically send crash reports to the developer of the app.
If everything above fails and you have paid for the app, you can report it to Apple and ask for a full refund. The instructions for the same can be found in this Apple Support article: