How would you detect a mouse click?

There's 2 ways of doing this, I recommend doing UserInputService. You could also use Player:GetMouse(), but I still recommend using UserInputService.

Player's Mouse

local player = game.Players.LocalPlayer
local mouse = player:GetMouse()

mouse.Button1Down:Connect(function()
	print(mouse.Target, mouse.Hit, mouse.ViewSizeX, mouse.ViewSizeY, mouse.X, mouse.Y)
end)

Mouse.Target and Mouse.Hit is 3D Space and X and Y is screen.

UserInputService

local UIS = game:GetService("UserInputService")

UIS.InputBegan:Connect(function(input)
	if input.UserInputType == Enum.UserInputType.MouseButton1 then
		print(game.Players.LocalPlayer:GetMouse().Hit) --// And the other things I showed in the other one.
	end
end)

Hope this helped!