how would I use math.random to make a randomizer?

Math.random you can use different ways. One of those ways, is to generate a number through another number. But you might notice, if you use it more than once in the same game/server, it will keep generating the same number. So you can use math.randomseed to make the numbers generate more random each time. Now it should be different every time.

This would be a part touched event.

math.randomseed(tick()) --Seeds the random number function by your local time.

debounce = false
local number = (math.random(1,3))
script.Parent.Touched:Connect(function()
if debounce == false then
if number == 1 then
    script.Parent.Transparency=1

elseif number == 2 then
    script.Parent.Transparency=0.5

elseif number == 3 then
    script.Parent.Transparency=0
end
debounce = true
wait (2) --Time you want before the next player can touch to change it
debounce = false
end
end)

This would be a part clicked event

math.randomseed(tick()) --Seeds the random number function by your local time.

local number = (math.random(1,3))
debounce = false
script.Parent.MouseClick:Connect(function()
if debounce = false then
if number == 1 then
    script.Parent.Transparency=1

elseif number == 2 then
    script.Parent.Transparency=0.5

elseif number == 3 then
    script.Parent.Transparency=0
end
debounce = true
wait(2) --Time you want before the next player can click to change it
debounce = false
end
end)