How to get to APF
To get there use a Whom-Pah to ICC and head northeast through a small tunnel in the wall of the ICC headquarters in Andromeda. Continue through the tunnel into a small valley, and on past that until you reach a large paved square landing pad with Unicorns at each corner. At the far end of the landing pad, there is a Unicorn Landing Beacon. Wait here until a shuttle comes (every 10 minutes). At this time a blue circular portal will appear at the base of the Unicorn Landing Beacon - step in.
Once in, head downstairs and you will find some NPC's there and a handy terminal which is the Unicorn Supply Depot (any faction can use it) which provides up to QL 125 medical supplies.
Be sure to have medical supplies.
Most NPC's are related to sectors 13, 28 and 35 waiting to reward you for items from the alien bosses. There is one which is silent and is rumored to be an NPC that will be used for upcoming sectors (if you traded a Data Core from an alien boss for Encrypted Kyr'Ozch Key with one of the NPC's, save it, many players believe they will allow access to them).
She is quiet, perhaps too quiet.
Now get on the bridge and follow the signs by turning left after the bridge, and you will arrive at an elevator. Right-click the elevator controls and you are now in the "staging area" of the playfields. You can talk to the Unicorn here to see how long till the gates open.
He will tell you when the gates open.
It's easy to get the aproximate time when he is going to let you into the Alien Playfields. Be aware his watch works in periods of 15 mins, so if he says 45 mins, it could be between 45-31 mins until the gates are open, and since the gates only remain open for 10 minutes, you should be there ahead of time.
Oh and if you're wondering why it takes so long for the gates to open...
To exit just go back top side, go past the bridge, turn left, go up the stairs and through a second bridge leading upstairs to a ship waiting for you to send you back to the landing pad in Andromeda. The ship will always be there, there is no waiting time.
Alright, now you know how to get to APF and exactly where to go to raid there, if you want more details about each sector check out the guides to Sector 13, Sector 28 and Sector 35 or about the loot that drops there.