Where to start
Read how to pick a random contest winner: preparing the list of entrants, setting up the draw, keeping a record of the result and making the draw transparent. When the list is ready, the random picker draws from it in your browser — up to 1000 entries, and up to 100 picks in one draw.
With or without repeats
Two kinds of draw are easy to confuse. Drawing without replacement means that nobody is picked twice: the right choice for prize winners, teams and turn order. Drawing with replacement means that every pick is made from the whole list, so the same entry can come up again: the right choice when everybody stays eligible in every round. Neither is fairer than the other. They answer different questions, and the picker does both.
Other ways to draw
For more entrants than a list can hold, number them and draw the numbers with the random number generator. For a choice between two options the coin flip is quicker, and for games the dice roller rolls the dice and adds them up. To see why a draw made by a generator is fairer than one made by hand, read what a random number generator is.