in general you don't

you can install harness or brackets for the new fan on the wood above the ceiling (given limited opening size, this may be a little tricky), then the fan (motor and fan) can be attached to the harness, and finally you put on the cove piece. 

More than often ,you will not be able to find a fan that fits exactly the same hole size, in that case you need some drywall work (either cut or patch).