why does the UDim2 property of an ImageLabel stay UDim2.new({0, 0},{0, 0})?

The problem seems to be on lines where you are sizing and positioning. UDim2.new doesn't take tables as arguments, you need to give it the coordinates as just numbers and not in the table. Calling UDim2.new with improper arguments will position/size the GUI at 0, 0, 0, 0.

UDim2.new(xScale, xOffset, yScale, yOffset)
--NOT this V
UDim2.new({xScale, xOffset}, {yScale, yOffset})

Fixed the problem for me.

#Nitpicks

##Inconsistency In some lines you use single quotes '' and in others you used double quotes "". Please choose one or the other.

##Deprecated methods You are using Instance.new second argument, the parent argument, which is deprecated. You can also read here for another reason not to use it.

local imageLabel = Instance.new("ImageLabel")
-- assign all properties
imageLabel.Parent = parent -- assign parent last
--NOT this V
local imageLabel = Instance.new("ImageLabel", parent)

##Strings vs enumerations

Use enumerations when applicable rather than strings. Reasons to use them here.

text_holder.Font = Enum.Font.Arial
-- NOT this V
text_holder.Font = "Arial"

#Final product

--use single quotes if you want to. I personally use double but it doesn't matter
local Dialogue = {}
local client = game:GetService("Players").LocalPlayer

function Dialogue.Create()
    if not client.PlayerGui.Game.Graphics.Dialogue:FindFirstChild("Holder") then
        local holder = Instance.new("ImageLabel")
        holder.Name = "Holder"
        holder.Image = "rbxassetid://2589083797"
        holder.Position = UDim2.new(0, 0, 0.671, 0)
        holder.Size = UDim2.new(1, 0, 0.329, 0)
        holder.BackgroundTransparency = 1
        holder.Parent = client.PlayerGui.Game.Graphics.Dialogue

        local text_holder = Instance.new("TextLabel")
        text_holder.Name = "Dialogue"
        text_holder.Size = UDim2.new(0.755, 0, 0.561, 0)
        text_holder.Position = UDim2.new(0.123, 0, 0.093, 0)
        text_holder.BackgroundTransparency = 1
        text_holder.TextColor3 = Color3.fromRGB(255, 255, 255)
        -- Color3.new takes arguments from 0-1, use fromRGB 
        text_holder.Font = Enum.Font.Arial
        text_holder.TextSize = 25
        text_holder.TextWrapped = true
        text_holder.TextXAlignment = Enum.TextXAlignment.Left
        text_holder.TextYAlignment = Enum.TextYAlignment.Top
        text_holder.Parent = holder 
    end
end

return Dialogue

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#Have a fantastic day.