How do I make a player spawn laying down?

Well, there are two things that I would try. First, I would do this:

game.Players.PlayerAdded:connect(function(player)
	player.Character.Humanoid.PlatformStand = true
end)

This toggles the "PlatformStand" property of a humanoid, which is often used to "trip" players or make them fall.

The second option is to use a rotation, which would be something like this:

game.Players.PlayerAdded:connect(function(player)
	torso = player.Character.Torso
	torso.CFrame = torso.CFrame * CFrame.fromEulerAnglesXYZ(90, 0, 0)
end)

I'm not exactly sure if those are the right numbers, I always play around with CFrame.fromEulerAngles() a bit before getting it right.

Hope this helps, or at least gets you further to figuring it out!