How can I reference the local player in a standard script?

Considering that you're using the script to get the person who clicked the brick's name,

.MouseClick should do the trick. https://www.robloxdev.com/api-reference/event/ClickDetector/MouseClick

script.Parent.ClickDetector.MouseClick:connect(function(player)
print(player)
end)

the output should be the person who clicked on the button's name ^ based on the example, you probably would already know what'd you need to do after that.

if you're trying to find the player's character, then just do

workspace:FindFirstChild(player)

if you're trying to find the player's player, just do

game.Players:FindFirstChild(player)

et cetera, the rest are self explanatory.

First: make a remote event anywhere, preferably replicated storage.
Second: Name the remote event "Event" and make a local script. in the local script do the following

game.ReplicatedStorage.Event:FireServer()

Third: Make a script in serverscript service. In the script write the following

local event = game.ReplicatedStorage.Event

event.OnServerEvent:Connect(function(player)
    print(player.Name)
    --Boom!
end)