Cleaning The Filter

It is good practice to test the water for ammonia and nitrite every day for several days after adding fish, no matter how many fish are already in the tank or how long it has been set up. By doing this, you are 100% sure the water is fine.
Once you have all your fish, go to testing once a week for a few months, then once a month. Then just test when you feel like it or if the fish start acting oddly. Testing the water is always the first thing to do when fish behaviour changes.

In theory, the filter media should not need cleaning immediately after a fishless cycle as there has been nothing in the tank to clog it up. But as soon as fish are put in the tank, fish poo, uneaten food and bits of plant, if there are live plants, get taken into the filter. There they decompose to make a brown goo which is a nitrate factory. This brown goo has to be cleaned off regularly by squeezing sponges in the old water you have removed during a water change or by swooshing round non-squeezable media.
The bacteria we need to keep live inside the biofilm which is attached to every surface in the tank. This biofilm takes a few months to fully develop so care should be taken when cleaning the media at first. Squeeze/swoosh the media gently. And use old tank water not tap water as chlorine in the tap water will kill the bacteria. In a few years it is probably safe to wash under the tap, but not with a new filter.
As for how often, that varies from tank to tank. To start with I suggest you look at the media at every water change. If there's not much goo, leave it till next time. You'll soon get to know how often you need to clean it.
Filter casing - the hard plastic bits - can be washed or even scrubbed under the tap.