First you need to vote for a delegate from your wallet. Then you get rewards just by having a balance in your wallet. There is no need for the wallet to be running all the time.

Ark is DPoS (delegated PoS). This means that only the delegates need to have their nodes running all the time (51 of them with the most votes). The rest just vote.

It's a good idea to check the wallet every now and then. If your delegate stops paying, it's time to change to a new one