How do I allow a player to teleport to a certain point when pressing a TextButton? (Solved)

You must define the player in the first example you gave. An example of what your script could look like.

Updated Script:

local player = game.Players.LocalPlayer
local SPAWNPOINTPOSITION = Vector3.new(-262, 589.8, 430)

script.Parent.TextButton.MouseButton1Click:Connect(function(player)
    local char = player.Character
    char.HumanoidRootPart.CFrame = CFrame.new(SPAWNPOINTPOSITION)
end)

Your old script was incorrect since you tried to get an undefined players character. All you had to add was a variable to define the player.

Your new script is correct since you are getting the character from the workspace:

local char = workspace[game.Players.LocalPlayer.Name]

but you could shorten the line with:

local char = game.Players.LocalPlayer.Character

.

Nevermind, solved it myself.

local SPAWNPOINTPOSITION = Vector3.new(-262, 589.8, 430)

script.Parent.TextButton.MouseButton1Click:Connect(function(character)
    local char = game.Workspace[game.Players.LocalPlayer.Name]
    char.HumanoidRootPart.CFrame = CFrame.new(SPAWNPOINTPOSITION)
    script.Parent.Parent.Parent.Visible = false --Added this line, don't worry about it.
end)

But please, feel free to improvise on this script. There might be a better way! I'd appreciate any help!

The issue with this script is that you're teleporting on the client instead of the server. To teleport on the server, you can use a RemoteEvent. Create a RemoteEvent called TeleportEvent and put it inside ReplicatedStorage and you can use the FireServer function to fire to the server and listen on the server with OnServerEvent.

The use of LocalPlayer is unneeded because the player gets passed by default when calling FireServer.

Local script:

local teleportEvent = game:GetService("ReplicatedStorage").TeleportEvent

script.Parent.TextButton.MouseButton1Click:Connect(function()
    teleportEvent:FireServer()
end)

Server script:

local teleportEvent = game:GetService("ReplicatedStorage").TeleportEvent

local position = Vector3.new(-262, 589.8, 430)

teleportEvent.OnServerEvent:Connect(function(player)
    player.Character:SetPrimaryPartCFrame(CFrame.new(position))
end)