It depends on the shuffle model, and if you are using automatic syncing to load the shuffle, or the manual (drag and drop items to the shuffle in iTunes) method.
This document shows the four types (and also explains the methods available to load a shuffle with songs)
If I assume you have the current 4th (or 3rd) gen shuffle, and you have been loading songs manually...
First, the latest iTunes many hide the sidebar. To show the sidebar, from the menu bar, under View, select Show Sidebar.
Select the shuffle in the sidebar, under DEVICES. Click the toggle (small triangle to the left of shuffle) to drop down its content list, indented under the shuffle. Select Music there. Over to the right, there is a list of songs currently on the shuffle. Select the song you want to remove and press Delete on keyboard. You can do this with one song, a selection of songs, or the entiire list (Select All from the Edit menu).
If you have a 1st or 2nd gen shuffle, or use automatic syncing with a 3rd or 4th gen shuffle, please post back.