NOTE: This guide was written in early 2019 and was correct and up-to-date at that time. Things change, however, so please leave a comment if anything needs to be added or changed.
How to get a large number of Darkmoon Prize Tickets with a minimal amount of time and effort:
[80 tickets] There are nine Darkmoon dungeon artifacts that can be turned in at the Faire for rewards. They give 5, 10, or 15 prize tickets apiece, and you can redeem one of each type per character per Faire. All can be purchased on the Auction House, usually for reasonable amounts if you wait until the prices drop.
[10 tickets] Kill Moonfang. Use the premade groupfinder to find a group. Can be done once per character per Faire.
[20 tickets] Do all five profession quests. They give 4 tickets apiece. Can be done once per character per Faire.
[120 tickets] Pet battles (guides here). Win both and you get 15 tickets. Can be done once per account per day.
[100 tickets] Fish up or purchase 100 Darkmoon Daggermaw and buy the Faded Treasure Map. If your classic fishing skill is high enough, fishing them should take 30-40 minutes. Can be done once per character.