Setting Up and Adjusting Pickups
Fret or capo all strings at the last fret. Raise the pickups up to where the pole pieces are just about touching the strings, evenly on both sides. Put a driver's license, business card, or similar between the pickup and strings. It should be held there by the string pressure.
While holding the guitar in the playing position, lower the pickup evenly by half turns of the height adjustment screws until the license falls free. That's the closest to the stings that you are going to want your pickups, otherwise they may hit the strings when you play hard. From this point, I would plug into a loud, and just a little overdriven, amp with plenty of headroom and start playing and lowering the pickups until they are in the sweet spot that results in the voicing you prefer. That will be different on every guitar and may be different across the stings/neck so you have a bit of compromise to make.
Always start with the neck pickup. It's much easier to get a good tone out of, and dial in, a bridge pickup to match the neck pickup than the other way around, so start with the neck. What you are really looking for is two things - that the magnetism of the pickup doesn't pull the stings too much and produce unwanted artificial harmonics (this mainly happens on neck pickups with stronger magnets, and that the long tail of the sustaining note evolves in a pleasing way as it decays. You will hear that note tail change in complex ways as it gets very quiet near the end of its sustain. That's why you want a loud amp, with a touch of gain, to enhance the ability to hear that. You can now try raising or lowering the pickup evenly on both sides by a half or full turn of the screws at a time to see what the overall tonal difference is. Pickups can be very sensitive and responsive to this. See what you like. You can make a pickup brighter/warmer and more or less dynamic by adjusting its height.
Once you get the overall height how you like it, you can adjust the height adjustment screws independently to angle the pickup in the ring. I tend to lower the bass side a bit to help enhance the unwound strings on most PAF-types, but it's totally a matter of preference and each guitar/pickup combination will respond a little differently.
Now that you've got the neck pickup dialed in, repeat with the bridge. Once you have that set, play a little bit while flipping the 3 way switch through all three positions. Adjust the bridge pickup, trying to get the balance of volume that you prefer in the neck and bridge positions (not everyone wants both pickups even) and also try to get a middle position sound that you really like. I do this part by adjusting the bridge pickup only and leaving the neck where I liked it best. I like to set them up for a great chirpy nasal honk on the note attack in the middle position. Some prefer more neck or bridge dominance when in the middle. After this, you’ll probably want to adjust your amp settings again, to match your new guitar/pickup sound. Adjust the amp while on the neck pickup. Always work on the neck pickup, then match the bridge to that. That's my theory. Step away from the room for a while to "re-calibrate" your ears to the world and then come back and repeat the fine tuning. Maybe even give it a few days or try in another room or rig. The mind can play tricks on you and "compensates" when you listen to the same thing for too long so it’s good to step away sometimes.
A note on adjustable pole pieces - use these to balance the sound of the individual coils in a humbucker or to favor specific strings. Raising the pole screws and lowering the entire pickup by the same amount will give you more of the sound of the screw coil. Doing the opposite will give you more the sound of the slug coil. This is preference here and also a matter of matching the pickups to the guitar. In your particular pickup set, you will likely find that you get a brighter sound by balancing the pole screws and height screws to favor the screw coils. You might get more chip/honk sound with the two coils closely balanced, and a warmer overall sound when you favor the slug coils. After setting the overall height of the pole screws, adjust for individual string balance.