Hi @BThoresen,
The starting point here is a calculation property: Create calculation and rollup properties
You would create such a property on the contact object and use the calculation method “Count” for associated tickets where the ticket status is open. Let me know if you get stuck at any stage.
Once created this is a regular contact property which you can use in report building. (If you need more help here, let me know what exactly the report should look like.)
This can also be achieved with a cross-object report and without a property but I found this to be a bit more reliable and also useful for further use (saved views, automated notifications etc).
Best regards!