This question frequently comes up on all forums. First as others have stated, Congratulations for taking up the flag. You are a needed addition to the hobby-sport.

As jester_s1 pointed out, the AMA Rulebook reference Special Events supplies a world of information. Now event 705, is the main Fun Fly guide. BTW: Please do NOT confuse the term "Fun-Fly" with the often stated, "Fly-In". "Fun Fly" denotes some form of COMPETITION. OTOH "Fly-In" denotes just a gathering of models/modelers for fun and games not into competition.

Now on to "RADIO CONTROL COMPETITION FUN FLY For event 705"

There are two important rules in that section of MANY suggestions.

One is: 2. General: These rules provide flight tasks suitable for unlimited time events as well as traditional mission-oriented, fun-fly tasks. They provide a variety of tasks from which a Contest Director can choose to define a challenging contest tailored for a given location, expected weather conditions and expected skill level of attendees.
The builder-of-the-model rule will not apply.

Two is: 8.2: Tasks may be announced prior to the contest or drawn at the contest. It is encouraged that a contest format has a variety of tasks. If the tasks are drawn at the contest, similar tasks (such as all looping tasks) should be placed together and drawn from once so that one type of task does not dominate the contest.
The CD may develop new tasks based on variations or combinations of the tasks below or using entirely new ideas for tasks. Unlimited tasks should be timed events, whereas Fun-Fly tasks are typically mission-oriented. Participant, official, and spectator safety should be considered when developing new tasks.

It all means that you can look over the presented ideas, and come up with your own. You can make it as simple or as complicated as you want. I like simple. I ran one for 12 consecutive years during the month of Feb. It has been dropped for the past two years however I am asking the club to let's start again next Feb. Sometimes it's cold and rainy sometimes clear, 70* and no appreciable wind.

Speaking of awards: My Fun-Fly had 4 rounds. Each round had 2 tasks to be performed on one flight. For example first round: Takeoff and allowed 30 seconds then idle or dead stick as pilot preferred. Task 1: glide to land at 30 seconds of glide. Deduct 2 points for each second over/under total 60 seconds flight time. Score landing at touchdown. Task 2: Touchdown in an area of concentric circles/squares for points such as 60-50-40-30-20-0

Most enjoyable event is 5 plane Out & Back Race. Flag drops with all engines running. Straight out for 15 sec. from flag drop. Time is back over a straight finish line. Points by finish place. The fast racer will not usually finish well.
#2 task is then all planes circle around, flag drops for a 3 minute balloon burst. have about 4 balloons attached to 8' of dowel sticks in different places. Models have a course to fly like a pylon race.
Spot landing, bomb drop, Limbo and several other items work well with this Fun-Fly.

Overall winners determined by numbering round winners with 1 point for each person they best in that round. The overall winner may well have flunked a round but had a barn-burning round so lots of points.

Awards then were percentages of the entry fees usually $10. Get 25 fliers and that is $250.00. 1st usually got 30% and such would be $75. Good day for a FUN-Fly. Club usually gets 15% but furnishes burgers, Hot dogs and such for the pilots and workers.
Even if the club treasury loses a few bucks, it is usually considered well worth the expense for hosting such a FUN-Fly competition event.