How can I add a player points system to my game?

I tried to make it with the local scripting way,doesn't work..

You should make it in a script not localscript:

-- declare service
local PointsService = Game:GetService("PointsService")
 
-- Bind function to player added event
game.Players.PlayerAdded:connect(function(player)
	-- Get total number of points the game has available
	local pointsToAward = PointsService:GetAwardablePoints()
	-- Get total number of points this game has already awarded to the player
	local universeBalance = PointsService:GetGamePointBalance(player.userId)
	-- Check if the game has points to award and if the player hasn't gotten any points yet. If both are true, then give the player a point.
	if ( pointsToAward > 0 and universeBalance == 0) then
		PointsService:AwardPoints(player.userId, 1)
	end
end)
 
-- Bind function to when points are successfully awarded
PointsService.PointsAwarded:connect(function(userId, userBalanceinUni, userBalance)
	-- Show message indicating that a player has gotten points
	local message = Instance.new('Message', game.Workspace)
	message.Text = "Point awarded to " .. userId .. ". This player now has " .. userBalance .. " points total!"
	wait(5)
	message:Destroy()
end)

also Thank the roblox wiki.

You should make it in a script not localscript:

view source

-- declare service

local PointsService = Game:GetService("PointsService")

 

-- Bind function to player added event

game.Players.PlayerAdded:connect(function(player)

    -- Get total number of points the game has available

    local pointsToAward = PointsService:GetAwardablePoints()

    -- Get total number of points this game has already awarded to the player

    local universeBalance = PointsService:GetGamePointBalance(player.userId)

    -- Check if the game has points to award and if the player hasn't gotten any points yet. If both are true, then give the player a point.

    if ( pointsToAward > 0 and universeBalance == 0) then

        PointsService:AwardPoints(player.userId, 1)

    end

end)

 

-- Bind function to when points are successfully awarded

PointsService.PointsAwarded:connect(function(userId, userBalanceinUni, userBalance)

    -- Show message indicating that a player has gotten points

    local message = Instance.new('Message', game.Workspace)

    message.Text = "Point awarded to " .. userId .. ". This player now has " .. userBalance .. " points total!"

    wait(5)

    message:Destroy()

end)