There's quite a few different ways, but I guess the overriding question is: what rank do you want to achieve and maintain?
My quick and brainless way for a moderate number of merits is to go to a rival power's control system and interdict/destroy ships until I have enough merits. Good for maintaining up to rank 3 if you're combat orientated.
But for anything other than my very limited playstyle,
A Lazy Commander's Guide to Powerplay is probably what you're looking for.