If you're in "Artists" view (where you see a list of artists down the left side of iTunes) just click the "random" button that's in the banner across the top of the song listing, near the artist's name (extra hint, hold down the option key to change whether those buttons replace the currently playing music or just add to it):
If you prefer "Songs" view, you can turn on the "column browser" (in the "View" menu), so you'll see lists of genres, artists and albums across the top of the iTunes window - then you can double-click an artist's name to add all the songs to the "play next" list, and click the "randomize" button that's next to the currently playing song (top center). If the music is already shuffled before you double-click, it remembers that.