How would I make the Character get faster as it moves?

What would I put in a script to make when the character moves it picks up speed? Would I use a loop to add to the players speed by increments?

You should indeed use loops and use increments, It isn't done completely in a loop because it would add to the speed when the player isn't moving, script is below, the explenation is too, if you need some more explanation, feel free to ask (btw mark this as answered please xD)

Script needs to be in workspace

Increment = 1 -- It will become this much faster every time
DelayT = 0.1 -- It will wait this time before it starts the loop again
defSpeed = 5 -- Starterspeed, this number will change trough the loop
maxSpeed = 100 -- If you don't want this set it to 99999999999999999999999 or something like that xD
Speed = defSpeed
plrWalking = false

game.Players.PlayerAdded:connect(function(player) 
	player.CharacterAdded:connect(function(char)
		player.Character.Humanoid.Running:connect(function(speed)
			if speed > 0 then -- player isn't standing still
				plrWalking = true
			else
				plrWalking = false
			end
		end)
	end)
end)

while wait(DelayT) do
	
	for index, player in pairs(game.Players:GetPlayers()) do
		char = player.Character or player.CharacterAdded:wait()
		hum = char:WaitForChild("Humanoid")
		if hum and plrWalking and Speed < maxSpeed then -- if humanoid and player is walking
			print("plr is running")
			Speed = Speed + Increment
			hum.WalkSpeed = Speed -- increasing speed
		elseif not plrWalking then
			Speed = defSpeed
			hum.WalkSpeed = defSpeed -- reset speed when stopped
		end
	end
end