Update the client as usual - download it from the Client Menu at the top of the screen https://www.tukui.org/download.php?client=win (Clicking OK when the client says there is an update, doesn't update the client, you need to download it from the link)
The drop down menu to toggle between Classic and Retails is the bottom right of the client. See the arrows in the screenshot.
Here is how it will look when one of the WoW versions is selected
Download and update addons as normal for each of the wow versions.