The 1st and 2nd gen shuffles do not "sync" like other iPods. Everything is loaded manually (or using the Autofill feature). The older shuffles also do not support multiple playlists, so everything you load is on one default "playlist" on the shuffle. The following applies to both the 1st and 2nd gen shuffles.
First, if you use the latest version of iTunes, it may hide the sidebar. To show the sidebar, from the menu bar, under View, select Show Sidebar.
Select Books under LIBRARY in the sidebar. Your audiobooks are shown on the list to the right. Find the book or books you want to put on the shuffle.
Without clicking on it, find the shuffle in the sidebar, under DEVICES. From the list of audiobooks, drag the desired book and drop it on the iPod in the sidebar. Alternately, right (Control) click on the audiobook on the list, and from the contextual menu, select Add to Playlist and target the shuffle. Using either method, iTunes loads the book on the shuffle. You can do this with one book or a selection of books at one time.
This puts the audiobook on the shuffle, but finding it while using the shufflle may be difficult, if you have a mix of many songs and one book on the shuffle. Here is how to overcome this limitation of the old shuffles.
Select the shuffle in the sidebar, under DEVICES. Over to the rignt, there is a "bar" that says Settings and On This iPod (I think it said Contents in previous iTunes versions). Click on On This iPod. You see a list of items currently on the shuffle. In the headings for the list's columns, make sure the left-most column heading (for the column with sequential numbers) is selected. This sorts the list in play order. Find your audiobook on the list, select it, and drag it to the top of the list, so it is first in play order. If you have more than one audiobook on the shuffle, put them all in desired play order at the top of the list.
When using your 2nd gen shuffle, put the "other" switch (the mode selector) in the play-in-order position (for a 1st gen shuffle, put power switch in the middle play-in-order position). Triple-press (three presses in a row) the center (play/pause) button, to "reset" the list being played. When the shuffle is in play-in-order mode, it jumps to the first item on the list. That is your audiobook.