I'll assume you have the current (4th gen) iPod shuffle.
The latest version of iTunes may hide the sidebar. To show the sidebar, from the menu bar, under View, select Show Sidebar.
In the iTunes sidebar, select the shuffle under DEVICES. Over to the right, there is a row of "tabs" (starting with Summary). Click on Music there. This Music tab is where you tell iTunes how to automatically sync songs to the iPod. Here's one easy and convenient way to set it up...
Create a new playlist in iTunes. You do this by clicking on the plus sign (then New Playlist) at the botton of the sidebar. Name it something like "iPod Songs" (or whatever you want).
Up above (in the sidebar), ciick on Music under LIBRARY. From the list to the right, drag ALL of the songs (including that new purchase) that you want from the Music library to that new playlist. You can keep the number of songs small for now, just so you know how this works...
Go back to the shuffle's Music tab, and set it to Sync Music. Below that, choose the option to sync based on Selected playlists, artists, albums, and genres. Below that, ignore everything except for the list of Playlists. Find and checkmark ONLY that new playlist with the songs you want on the shuffle. When you click Apply, all of the songs on that playlist sync to the shuffle.
NOTE: If there are songs on the shuffle already, they are replaced by the selection on the Music tab.
Going forward, to update the songs on the shuffle, just update that playlist (add and remove songs). The iPod does not even need to be connected. The next time you connect the shuffle (or click the Sync button), all changes since the last time sync automatically.
This document has general information about loading content on shuffles, including doing it manually and with the Autofill feature.
http://support.apple.com/kb/HT1719
If you have any specific questions, please post back.