How do I make this rotate on key down R?

		mouse.KeyDown:connect(function(key)
				if key == "R" then
					NewTurret.Orientation = Vector3.new(X0,Y+90,Z0)
				end			
		end)

You asked: How do I make this rotate on key down R?

Firstly, we must use the UserInputService which can detect user input via the keyboard.

local UIS		= game:GetService("UserInputService");

UIS.InputBegan:Connect(function(key, gpe)
	if (not gpe) then
		if (key.KeyCode == Enum.KeyCode.R) then
			NewTurret.CFrame = NewTurret.CFrame * CFrame.Angles(0,math.rad(90),0);
		end
	end
end)

This will rotate the turret 90 degrees on the Y axis. Always use CFrame.Angles() when dealing with rotation. In my example I'm assuming NewTurret is a part, or an object that has a CFrame. If it's a model you could use

local UIS		= game:GetService("UserInputService");

UIS.InputBegan:Connect(function(key, gpe)
	if (not gpe) then
		if (key.KeyCode == Enum.KeyCode.R) then
			NewTurret:SetPrimaryPartCFrame(NewTurret.PrimaryPart.CFrame * CFrame.Angles(0,math.rad(90), 0));
		end
	end
end)

Although when using the provided code above you must have the primary part set already on the model. math.rad() takes an argument in degrees and converts it to radians which is what CFrame.Angles() uses.

Maybe??

local UIS = game:GetService('UserInputService')

UIS.InputBegan:Connect(function(key,gpe)
	if key.KeyCode == Enum.KeyCode.R and not gpe then
		local NewTurret = workspace.Part -- Remove this since you already have a variable for it
		NewTurret.Orientation = Vector3.new(X,Y+90,Z)
	end
end)