How do you change someones team randomly?

Yes, you can do this using the math.random function. This function takes in two arguments and returns a randomized number between them.

Setup a randomized wait time, as well as the random character to change teams, and randomly manipulate the team they reside in.

local minWait = 10
local maxWait = 50

while wait(math.random(minWait,maxWait)) do
	local currentPlayers = game.Players:GetPlayers() --Collect all players
	local currentTeams = game.Teams:GetChildren() --Collect all teams
	--Get a random player, and a random team
	local randomPlayer = currentPlayers[math.random(1,#currentPlayers)]
	local randomTeam = currentTeams[math.random(1,#currentTeams)]
	--Manipulate the random player's team to the random team.
	randomPlayer.Team = randomTeam
end

Note: In order to ensure the randomized team will not be the same as the randomized player's current team, you will have to add a while loop.

while randomPlayer.Team == randomTeam and wait() do
	randomTeam = currentTeams[math.random(1,#currentTeams)]
end

randomPlayer.Team = randomTeam