Click script?

First add a Click Detector to the Part then do this

EX.

local Part = script.Parent
local ClickDetector = Part.ClickDetector

ClickDetector.MouseClick:connect(function(Player)
    Part.BrickColor = BrickColor.random()
end)

Like the other answer add a Click Detector then do this:

local p = script.Parent
local cd = script.Parent.ClickDetector

function onClicked()
p.BrickColor = BrickColor.random()
end
cd.MouseClick:connect(onClicked)

If you don't want to use a click detector, try this:

wait()
local mouse = game.Players.LocalPlayer:GetMouse()
mouse.Button1Down:Connect(function()
    if mouse.Target = game.Workspace.DesiredPart
    game.Workspace.Baseplate.BrickColor = BrickColor.rand
    end
end)

DesiredPart is the part that you want the button to be.