How do I teleport players to random spawn on a map?

In the future, please do include as much information as possible in your post, and be sure to atleast format your LUA code.

I do not know your script's context, but from what I see, you're using LocalPlayer in a script, which cannot be done.

Now, lets start from the beginning:

local Spawns = game.Workspace.Spawns:GetChildren() 
local RandomSpawn = Spawns[math.random(1, #Spawns)] 

Those two lines are perfect, good job!

Now, from the title of your thread, you've led me to believe that you want all players to be teleported to a random spawn. We can accomplish this by creating a *Players *table. After that, we just need to iterate through the our "Players" table, and teleport them.

local Spawns = game.Workspace.Spawns:GetChildren() 
local players = game:GetService("Players"):GetPlayers() --GetPlayers returns a table with a list of all the players.
for index, player in pairs(players) do
	--We use forloops to iterate through tables.
	--You can read more about them here: http://wiki.roblox.com/index.php?title=Loops#For

	local RandomSpawn = Spawns[math.random(1, #Spawns)]  --Create a new randomspawn area for each player. (The loop will run for #players)
	local isPlaying = player:FindFirstChild("Playing") --Variable for your value in the player
	if isPlaying and isPlaying.Value == true then  -- Check if its in the player and that the value is true
		if(player.Character and player.Character.Humanoid and player.Character.Humanoid.Health >0 ) then --Check if the player is not dead
		player.Character:MoveTo(RandomSpawn.Position) 
		end
	end
end

FilteringEnabled on? Problem solver: Remote events/Functions

1. Insert a RemoteEvent in ReplicatedStorage, or anywheres which can be accessed both by the Client and the Server.
2. We'll name this RemoteEvent teleportation event

Now, we need to make this event fire each time we want to teleport a player to a certain location!

Since we'll be using this in a remoteEvent, we need to simply use the :FireClient() method, and not the :FireAllClients() method. (Although we could do it both ways if we did this differently...! )

This will be the ServerSideScript

local Spawns = game.Workspace.Spawns:GetChildren() 
local players = game:GetService("Players"):GetPlayers() 
local remoteEvent  = game:GetService("ReplicatedStorage"):WaitForChild ("RemoteEvent")

for index, player in pairs(players) do
	local RandomSpawn = Spawns[math.random(1, #Spawns)]  
	remoteEvent:FireClient(player, RandomSpawn) 
	
end

This will be a localscript, located in the StarterPack

local remoteEvent  = game:GetService("ReplicatedStorage"):WaitForChild ("RemoteEvent")


function functionName(...)
	local Tuple = {...} --The arguments here are in form of a tuple(This is just a table with all your paramaters)
	local player = Tuple[1]
	local randomspawn = Tuple[2]
	
	local isPlaying = player:FindFirstChild("Playing") 
	if isPlaying and isPlaying.Value == true then 
		if(player.Character and player.Character.Humanoid and 			
     		player.Character.Humanoid.Health >0 ) then --Check if the player is not dead
		player.Character:MoveTo(randomspawn.Position) 
		end
	end
end



remoteEvent.OnClientEvent:connect(functionName) -This will fire when we fired it from the server-side script. We use OnClientEvent, since we pushed a client method.

If you encounter any errors with the Script, be sure to let me know so I can fix them. I know I didn't really explain the RemoteEvent things very good, but I'm short on time, so...