As has been said the best way is to get media materials from the power contact in your Power's home system. Each power names this a bit differently, can't recall what the older Duvall calls them. You then look at the Power Play board for your pledged power and find a system that they are expanding into - just look at the list and pick the closest one. Then take your media materials (again whatever they are called) to a station in that system and again go to Contacts - Power and unload them.
Another important thing - you can't get the Power Play module (shield/weapon/etc) until you've been pledged for 4 weeks. So during your 3rd week, before midnight Wednesday night (game/UTC time) make sure you've done your 750 merits - that will then put you at Rank 3 which is what's needed to buy the module you want. If you do 750 merits in week one they will be halfed at week 2 and again at week 3. If you do them during week 3 you'll start week 4 at Rank 3, you can buy your module and then defect.
What I did was buy the module, say 2-6 of them depending, store them then defect. For example I got 1 FSD missile, a Prismatic shield in every size, 6 Packhound missiles, etc. I figured I might go nuts and slap 6 Packhounds on my Anaconda sometime, they are so damn fun to fire. I'm just about to get the Pacifier Frag Cannon from Hudson which will complete every Power Play module for me - well save for the mining lance, I mean really - do I care about that?!?
As has been said Fastracking your media materials is the fastest way but it's, in typical Frontier fashion, a grindy long process as you can only Fast track 10 at a time, and they are $10,000 - each. So 750 merits will cost you roughly $7.5M then the cost of the module(s). Oh and FYI once you've unlocked the module you can buy it at any station that has outfitting, period (you do get the 10% discount at Li Yong Rui stations though). Oh and once you defect you can't buy them any more unless you pledged and waited the month again (and did merits). So buy what you want and store while you can.
Make sense? Also realize that each module has a up and down side, the Prismatics are strong but are double the weight of a standard shield...
~X