How do I make a blood puddle when someone gets hurt?

First of all create a localscript and put it in the player, once you've done that set up an anonymous function to fire when the humanoid takes damage.

local hum = script.Parent.Humanoid
local LastHealth = hum.Health
local maxSize = 5 -- Determines the maximum size of the blood pool

script.Parent.Humanoid.HealthChanged:connect(function(Health)
	local change = math.abs(LastHealth - Health) -- this will let us create a bloodpool proportional to the change ofHealth
	if LastHealth > Health then
		local Pool = Instance.new("Part", game.Workspace) -- creates the new part and sets it's values
		Pool.Anchored = false
		Pool.BrickColor = BrickColor.new("Bright red")
		Pool.FormFactor = "Custom"
		Pool.Size = Vector3.new((change/hum.MaxHealth)*maxSize, 0.2, (change/hum.MaxHealth)*maxSize) --Defined maxSize on Line 3 of the script, make it what ever you want. 
		Pool.TopSurface = "Smooth"
		Pool.BottomSurface = "Smooth"
		Pool.CFrame = CFrame.new() + script.Parent.Torso.CFrame * Vector3.new(0, -3, 0) -- should place it below the players feet.
		--Optional add a mesh here to make it round.
		Pool.CanCollide = false;
		Pool.Touched:connect(function(hit)
			if not hit.Parent:FindFirstChild("Humanoid") then
				Pool.Anchored = true
			end
		end)
		Spawn(function()		-- spawns this function on a separate thread so it doesn't stall this one
			wait(60)
			Pool:Destroy() -- destroys the pool after 60 seconds.
		end)
	end
	LastHealth = Health -- sets LastHealth to Health so that next time the script runs change can be calculated correctly
end)

Try this out and see if it works :).

To make this work for all players add a script to the workspace, then add a localscript to that script with the disabled property checked. Add the above code to the localscript.

In the script use this code

game.Players.ChildAdded:connect(function(Player) -- fires when a player joins the game
	Player.CharacterAdded:connect(function(Character) -- fires when it's character is added
		local poolScript = script.LocalScript:Clone() -- clones the localscript
		poolScript.Parent = Character -- parents it to the character
		poolScript.Disabled = false -- enables it
	end)
end)

What this will do is clone the localscript containing the pool code into each of the players characters when they join the game and whenever they respawn.

EDIT: So I've compiled the localscript at the top for you, it's in one part now.

Layout in Explorer:
Workspace
-Script (2nd codeblock goes here)
--LocalScript (1st codeblock goes here)