I have purchased many songs from itunes...I need to put them on my shuffle, how do I do that?

There are several ways to load songs, whether they are purchased or added to your music library from other sources.

Manually load songs - Select shuffle in iTunes (click its device button on horizontal bar) so that you see its settings screen in iTunes window. Along left side (in the sidebar), under Settings, click Summary (probably selected already). To the right, the shuffle's main settings are shown. Find the checkbox for Manually manage music. If it's not already checked, checkmark it and click Apply. (Your shuffle may be set this way already.)

To load songs manually, show your iTunes music library in iTunes window (click Music button at left end of horizontal bar). Near the middle of horizontal bar, click Playlists. A sidebar appears along left side of window, with your shuffle listed under Devices. You can view your music library as desired using the control at right end of horizontal bar (I like using the Songs view to show a plain song list). From your library song list, click-hold-drag a song to the sidebar and drop it on your shuffle. You can do this with more than one song selected at a time. Alternately, instead of dragging/dropping, right-click selection and Add to Playlist -> [name of shuffle].

Use Autofill - Another way to quickly fill the shuffle completely is to use Autofill. Select shuffle in iTunes to show its settings screen. In the sidebar, under On My Device, click Music. To the right, the songs currently on shuffle are shown.

SIDE NOTE: To manually remove songs from shuffle, on this list, select song you want to remove and press Delete on keyboard. Song is removed from shuffle (not from your library). You can do this with more than one song selected.

At the bottom of shuffle's song list, the controls for Autofill are shown. Next to Autofill button, click Settings. Checkmark the boxes for Replace songs when Autofilling AND Choose items randomly, and OK. Over to the left, set it to Autofill from: Music. When you click Autofill button, iTunes puts a randomly selected set of songs from your iTunes music library on the shuffle, to fill it completely. Each time you do this, you get a new random set of songs. You can also set it to Autofill from one of your playlists.

Use automatic syncing - iTunes keeps shuffle "in sync" with a selected portion of your iTunes library. For example, iTunes syncs one or more playlists (in your iTunes library) with shuffle, each time you connect shuffle; iTunes updates shuffle with changes you make to those playlists. If you want more details about this method, please post back.