Consider the following situation:
You attack a highly defended target and get jumped by some MiGs. You manage to kill the MiGs, but on the way home, you realize that you cannot make it back. All of your fuel has been used in the dogfight. Now you have two options:

Either climb up and fly towards your home or alternate (if there is one) base and try to coax every last mile out of what is left in the jet in the hope that you can make it back, or fly to the nearest tanker and refuel your jet so you can get home safely. Let's assume that the base option is a no go. Your only remaining option is to find a Tanker and get some fuel into your jet before you flame out so you are going to make a triumphant return to you base.

You should ask AWACS for a vector to the tanker, or look up in your DED if there is a waypoint asigned for refueling. If AWACS tells you the vectors, you should also set your TACAN channel to the tanker's TACAN station. This will make finding the tanker much easier.

Once you have the tanker in sight, tell the pilot you would like to refuel. The tanker will transit from it's orbit into a refueling pattern. He also might descent, so watch what he is doing. As you approach the tanker, get behind it in approximately 500 ft and tell the pilot that you are ready for refueling. Make sure you are flying the same speed and heading as the tanker, but you have to be slightly below it. Do not place the horizon line in your HUD on the tanker during your approach. You will end up too high, not being able to descent without speeding up and overshooting the tanker. This is the pre-contact position.

Now you will see the boom extending from the tanker's tail. Gently steer towards the centerline of the KC-10 and watch your closure rate towards it. The 12 o'clock HUD view is usually the best view to see the tanker above you. Do not make big movements, Most pilots fly this maneuver with only two figers on the joystick...

There is no sense in using your RPM setting in the HUD as a reference. This is not fine enough. Look at the Fuel Flow gauge on the right side below the DED. You can make very minute adustments with your throttle (about 50 lbs/hr). Every little adjustment results in your jet speeding up or slowing down. Never use your spedbrake once you are attempting to contact the tanker. You will fall back and in the worst case, lose some altitude. Then you have to start all over again.

Now you should be able to see the two director lights on the tanker's belly. The left light tells you to go either up or down, while the right light tells you to go forward or aft. The lights tell you where you are in respect to the tanker's boom. If the right light is moving aft towards "F", then you have to slow down a little to fall back. If the left light is moving forward towards "U",then you are too high and have to descent a litle.

Do not try to chase the director lights, if you have made a good approach to the boom, you will find yourself already in the correct position and all director lights are green. You then should notice a little bump as the boom contacts with your air-refueling probe.

After you are finished refueling (either you tell the tanker that you are finished, or it will disconnect by itself as soon as your tank is full), slightly move left of the tanker to make room for your wingman to refuel. Stay in formation with the tanker as you did in your pre-contact posion, but stay on the left side of the tanker. Once your wingman is refueled, the tanker will break away to it's original orbit and you are good to go. However, if you are carrying external fuel tanks, only your internal tank is refueled in an A/A refueling.

For reference purposes the Wildcats procedure for AAR (as per the Falcon checklist) is as follows:

1. Radio - Request refuelling
2. TACAN - Select Tanker TACAN channel (via ICP or Backup Control)
3. TACAN Mode - Set A/A TR
4. Heading - Course to Intercept (HSI)
5. Altitude - Tanker ALT - 1000ft
6. Master Arm - check SAFE
7. Sensors - Check Nose Cold (Prior to Pre-Contact)
8. Refuelling Door - Open
9. Pre-Contact - Check AR/MS Light On and advise ready
10. Boom Operator - Follow instructions and lights
11. Refuelling - Hold position
12. Fuel - Check fuel transfer (gauges)
13. Disconnect - Refuelling door closed
14. Radio - Advise refuelling complete

This might sound easy when you read this, but it is very hard to fly. One way that has often been suggested is to lock up the tanker with your radar, but make sure you have the "Master Arm" switch set to sim. After you feel comfortable with it, try the same procedure without using your radar. Just fly under the tanker by slightly adjusting your fuel flow and watching the movement of the tanker. You will find it easier, the more you practice.