I have a Art Tech Cessna electric parkflyer that Has a broken Antenna from the receiver. What is the best way to re-attach this wire to the circuit board?

First you have to clean the hole in the printboard. A solder iron heating the area carefully for 1-3 sec and push out the remainings. If the hole isn`t open yet you should use a solder-sucker on the opposite side of the hole, heat the solder and suck away the rest.
If you have not lost any lenght of your antenna just strip of 3-4 mm of the isolation, twist the copperend firm and heat it and soak with solder. Put this end into the hole on the print, heat for 2-3 sec and add al ittle solder. This should do it.
Take care:
- Not to heat for a long time
- Not to waste solder on the wrong place
- Not use too much solder on the joint, it should look like a vulcano, NOT a pearl!