How to make these variables show as a string?

Your problem is because you're defining the variables before pressing the button, everything is empty. You should do this...

local player = game.Players.LocalPlayer

sendButton.MouseButton1Down:Connect(function()
	local gui = script.Parent
	local remote = game:GetService("ReplicatedStorage").RemoteEvent
	local textbox = gui.Main.DetailsBox.Text
	local sendButton = gui.Main.Sender
	local name = gui.Main["Name/IDText"].Text
	local method = gui.Main.Method.Text
	local price = gui.Main.Price.Text
    local message = "Discord Name/ID: "..name.."\n".."Payment Method: "..method.."\n".."Price: $"..price.."\n".."Details: "..textbox
    remote:FireServer(message)
end)

--serverscript
local Discord = require(3427317493)
local Webhook = Discord:GetWebhook("it had the proper webhook just removing this for safety")
local repStorage = game:GetService("ReplicatedStorage")
local remote = repStorage.RemoteEvent

remote.OnServerEvent:Connect(function(plr, message)
    Webhook:Post({Content = message})
end)

Edit: If it didn't work, don't hesitate to tell me.