That article describes all the ways to sync music to your shuffle.
The first step is to run iTunes and connect your shuffle. In iTunes, there is a sidebar on the left side of the window. You should see DEVICES, and your shuffle should appear under it. Select your shuffle in the sidebar.
Over to the right, you should see two "tabs." The first one is Summary and the second one is Music. Click on Music. At this point, take a look at that article in the section Syncing music automatically to iPod shuffle (3rd and 4th generation). Once you have it (the Music tab) set up to tell iTunes what to sync to your shuffle, every time you connect the shuffle, it will sync any changes you have made since the last sync automatically.
Another convenient way is to use Autofill. Again, start with the iPod selected in the iTunes sidebar, under DEVICES. You should see a list of content types indented under the shuffle (if you don't see it, click on the shuffle again). Select the one that says Music. Over to the right, you will see the music that is currently on the shuffle. At the bottom of the list, there are controls for Autofill. At this point, take a look at that article in the section, Syncing music using Autofill to iPod shuffle (3rd and 4th generation). You can Autofill from your entire music library, or from a playlist that you set up with only the music you want on the shuffle.
The third way is to manually drag songs to your shuffle, in the iTunes window. This is the way a lot of people use, but I think it is the least convenient. In the article, it is the section Syncing music manually to iPod shuffle.