How would I transport a player to one of the 10 parts I have named a certain name?

Hello there, I am glad to see that you are already on the path to success. I am only here to give you the little push that will allow you to create this program. First of all, because this is a text button that you are scripting, I recommend that you use a LocalScript. All GUI manipulation should take place on the client (with LocalScripts). I am going to assume that you will place this LocalScript into the button. All the things we need for this to work are the player, the button, and a random number. The player can be found by using the LocalPlayer property of the Players service.

Here is an example script of what we have so far:

local players = game:GetService("Players") 
--[[ 
    This is the recommended way to get 
    the players service, especially 
    from a LocalScript.
--]]
local player = players.LocalPlayer 
-- getting the player with the LocalPlayer property
local button = script.Parent 
-- assuming that the script is a child of the button
--[[
    Here we will add the clicked event
    so that when a player clicks on the
    button, it will call the connected function.
--]]
button.MouseButton1Click:Connect(function()
    local randomNumber = math.random(10) 
    --[[ 
        if you use one argument, such as ten, 
        it assumes that you are starting at 1.
    --]]
end)

Now comes the simple element of finding the part, and teleporting to it. I am going to assume that all of the parts are in the Workspace. Roblox provides a nice little method for finding certain parts by their name called Instance:FindFirstChild. Because you have named all of your parts the same thing except for the number, it is a simple matter to find a random part via concatenation.

Using all of the elements I have mentioned here, let us put together our script for getting the random part (adding on to our previous script):

-- assuming the rest of the script is up here
button.MouseButton1Click:Connect(function()
    local randomNumber = math.random(10) 
    local randomPart = game.Workspace:FindFirstChild("Spawn"..randomNumber)
    --[[
        So if random number were 3,
        randomPart would be the part
        in the workspace with the name 
        of Spawn3. This is possible because
        of the ".." concatenation operator.
    --]]
end)

The only thing left to add, is the actual teleportation of the player. For this, we will use the HumanoidRootPart of the player's character. To teleport, we need only change the position of the HumanoidRootPart to that of the brick, plus a few y studs of offset.

Final script:

local players = game:GetService("Players") 
local player = players.LocalPlayer 
local button = script.Parent 
button.MouseButton1Click:Connect(function()
    local randomNumber = math.random(10) 
    local randomPart = game.Workspace:FindFirstChild("Spawn"..randomNumber)
    local humanoidRootPart = player.Character.HumanoidRootPart
    --[[ 
        we don't need to wait for the character,
        because players cannot click if they are 
        not loaded in. 
    --]]
    humanoidRootPart.CFrame = CFrame.new(randomPart.Position.X, randomPart.Position.Y + 5, randomPart.Position.Z) 
    --[[
        CFrames are the recommended 
        method for teleportation.
        I added an offset of five, you can 
        change that if you wish
    --]]
end)

I hope this helps. Have a great day scripting!

More info on...

• CFrames

• Teleportation

• Getting Player Position

If you need anymore information, feel free to comment below. I will do my best to help.

The most efficient way to do it would be:

--localscript inside of the button

local players = game:GetService("Players")
local player = players.LocalPlayer
local playergui = player.PlayerGui
local character = player.Character or player.CharacterAdded:Wait()
local humanoid = character:WaitForChild("Humanoid")

local spawns = game.Workspace:WaitForChild("Spawns") -- folder that holds all the parts

local positions = {} -- table that will hold all the possible positions of the spawn parts

math.randomseed(tick()) -- make it random for each client

for _,v in pairs(spawns:GetChildren()) do
    table.insert(positions, v.Position) -- inserting the positions of the spawn parts into the aforementioned table
end

local debounce = false
playergui.SCREENGUINAME.BUTTONNAME.MouseButton1Click:Connect(function()
    if not debounce then
        debounce = true -- to stop spamming
        local randomPos = positions[math.random(1, #positions)] -- randomly picking 1 value (position) from the table
        character:MoveTo(randomPos) -- moving the character to the chosen position
        print(unpack(positions)) -- just for fun; printing the positions of the spawn parts
        humanoid.Died:Connect(function() -- when the humanoid dies
            debounce = false -- allow the button to be clicked again
        end)
    end 
end)

Of course change "SCRENGUINAME" and "BUTTONNAME" to the actual names you used (which you probably already know). These are all of the methods used, to take a closer look:

MouseButton1Click

debounce

math.randomseed(tick())

MoveTo

Humanoid.Died

in pairs

Its simple, in math.random on teleport you need to use SpawnsLocations:GetChildren()[math] for get the block.

This literally as said will get everything it has inside a location through a numerical value. you can choose the numerical value and start your function(If you do not understand my explanation tell us the comments. my english is very bad, Or if have something wrong, also tell me in the comments.)

Here is a example:

-- Local Script
local player = game.Players.LocalPlayer -- Get player
local char = player.Character or player.CharacterAdded:Wait() -- Get player character

local SpawnsLocations = game.Workspace.Spawns:GetChildren() -- Add :GetChildren() / Get all in Spawns folder
local value = math.random(1,#SpawnsLocations) -- Get random number with 1 to length of spawns location.
if SpawnsLocations[value] ~= nil then -- Check if spawn is not nil
    print("Spawn found!")
    -- Teleport
    char:WaitForChild("Humanoid") -- For no errors on teleport.
    char:MoveTo(SpawnsLocations[value].Position) -- Move player to selected part
end

Wiki pages:

GetChildren

math.random

Hope it helped :)