It depends on what power you are pledged to.
If you're pledged to Arissa L-Duval or another combat oriented power go to any of their expansion systems and there will be political conflict zones. You get 10 merits per kill this way.
If you're pledged to anyone else either A) Go to Hudon's expansions zones and oppose his expansion (10 merits per kill) or B) Go to any hostile PP factions space (If you're pledged to an Empire power go to Fed / Alliance or Independent, Likewise if you're pledged to a Fed power go to anything but fed space) Interdict ships aligned with hostile powers and kill them. (30 merits per kill)
If you wish to undermine a power that is not hostile to you. E.G you're Aisling Duval and you want to undermine Denton Patreus. You will have to interdict his ships and steal their cargo and bring the cargo back to your PP factions systems. But it is important that you do not kill them or you will lose merits. (5 merits per tone of cargo recovered, -10 merits per kill if you kill the target I think)
