Try the latest DAVx⁵ version. Use the latest version of your server software, if applicable.
Read the Tested services, FAQ and Manual pages carefully. The most common issues are explained there.
Try the forum search – most questions have already been answered.
Have a look at the debug info/error details/logs. You can often get an idea what’s the problem yourself.
Make sure that it’s not a server or networking problem. Have a look at your server logs and search the FAQ/forums/bug tracker of your server software, too.
When posting, please provide as much information as you can:
debug info (see below),
steps to reproduce (what you tried to achieve and what your problem is),
your environment: server software (including version), do other clients work, etc.
How to get debug info:
If you get “No CalDAV/CardDAV service found” when you try to add an account: tap “View logs”.
If you get an error notification while synchronizing: tap the notification. A debug info activity will appear.
Otherwise, use DAVx⁵ / Settings / Debug info.