@Sonny61 For damaged items, you can initiate a request for compensation at https://airbnb.com/resolutions
If the guest doesn't voluntarily choose to pay (which, of course they won't) you will need evidence such as photos and receipts to escalate the claim for repairing or replacing the damaged items. Generally this process is only worthwhile when the stuff at stake is very expensive and not normal wear and tear (e.g. stained linens).
Theft, on the other hand, is much harder to prove. If you believe that the guest intentionally stole valuable items from the home, the first thing you need is a police report.