The Trakt servers are now back online! 
In most cases, things should just start working again automatically. However, if scrobbling and/or sync is not working, you may need to sign out of Trakt and sign back in through Infuse. This is due to some session tokens being lost on the Trakt site when the database corruption occurred.
Infuse does not sync prior watched history (items watched before logging into Trakt), so unfortunately this means you may need mark some items as watched manually on the Trakt site which were played after December 11th.
If you are missing watched history for items that were watched before December 11th, you can try recovering this data through the Trakt dashboard.