See the player who fiered RemoteEvent? ( Easy )

ServerScript

script.Parent.MouseButton1Click:Connect(function()
		game.ReplicatedStorage.Race:FireAllClients()
end)

LocalScript

game.ReplicatedStorage.Race.OnClientEvent:Connect(function(player)
	print(player) -- Obviously this didn't work, but how can I make it work?
end)

If you need more context - the Player will click a SurfaceGui Button that is in the workspace, It will announce that the race has started. Everyone in the server will get a TextLabel popup saying that the Race has been started by Player.

You have it backwards.

The LocalScript should look like:

script.Parent.MouseButton1Click:Connect(function()
        game.ReplicatedStorage.Race:FireServer()
end)

The ServerScript should look like:

game.ReplicatedStorage.Race.OnServerEvent:Connect(function(player)
    print(player.Name) -- Obviously this didn't work, but how can I make it work?
end)

If you want it to print the player's name, you need to use the name property of player.

print(player.Name)

Hope this helped you!