You can do this by prefixing the table with the database name. For example, the trigger in db1 can run something like "INSERT INTO DB2.dbo.TableName(column1, column2)....".
However, I would not recommend this. Cross database triggers may be little risky. If the other database is not available or busy, it can delay or abort your transactions.
I would recommend replication or an asynchronous trigger using Service broker for this type of requirements.