A vital part of each fantasy draft is the position that your team drafts from. If an owner is well prepared with many mock drafts under their belt, they may now which pick they want in order to get their desired players. That being said, the number 1 pick is always coveted because it ensures a fantastic player.
Depending on the league, winning the draft sweepstakes will either grant you the first pick automatically or let you pick a spot in the first round that you desire.
The most common way that leagues determine the draft order is at a draft party, unless they let the computer randomly generate the selection. When actually picking the order you could almost do any random or competitive activity. Draw from a hat, play a game of musical chairs, have a cornhole tournament, or just have a good ole' fashioned arm wrestling competition. The possibilities are endless!
So you can't hold a draft party? No big deal. You could stick with the competition aspect by betting on athletes in tournaments. Even having a video game contest can get the job done.
If you want it to be more up to chance to even the odds, having a rubber duck or snail race is a fun, nerve racking way to get a winner.
Lastly, if your league is more intense and is a keeper or dynasty league that carries players over from year to year, you could just use the previous years standings to determine the order, like the NFL does.