Here's what the iPod shuffle's manual says about putting podcasts on the player:

Part of the appeal of listening to podcasts on an iPod is that new episodes can be automatically transferred to the iPod. Although Apple says you must manually drag-and-drop podcasts onto the shuffle, you can help automate this process by creating a Smart Playlist for recent audio podcasts in iTunes.

1. First, to make sure your podcasts are transferred during an Autofill, select Podcasts frmo the source panel. Select All and then click File > Get Info. Change Skip While Shuffling to No.
2. Choose File > New > Smart Playlist...
3. Complete the Smart Playlist like the screenshot below. Click the + button to add the rules. Click OK.
4. Type a name for the playlist you just created. I named mine Podcasts for Shuffle.
5. Connect iPod shuffle. Select the iPod in iTunes Devices panel and click the Contents tab.
6. At the bottom of the window, select the playlist you just created from the Autofill from menu.
   
7. Click the Autofill button. It may take several minutes to transfer the podcast files.
8. You probably want to listen the newest podcast episodes first. Let's sort the audio files by the date they were added to iTunes library. Right click the Name column header and select Date Added. Then click the newly displayed Date Added header to sort newest-to-oldest. To manually change the order of the episodes, click the first header (which is only labeled with an arrow). Then simply click and drag the titles up or down the listing.
9. Once the order is to your satisfaction, iTunes should automatically update the iPod. You can manually update the order on iPod shuffle by choosing File > Sync Songs.
10. Disconnect and enjoy the podcasts! Let's hope that the podcasters announce the podcast title and episode topic at the very beginning of each episode so you know immediately what you are listening to (and if you want to skip it).

Next time you connect iPod shuffle, you can simply click Autofill to have the newest episodes added to the beginning of iPod's list.

But....

You probably want to listen to some podcasts and songs on iPod shuffle. While you can't automatically update podcasts in the same way above, I'll list how to organize both podcasts and songs for iPod shuffle.

1. Choose File > New > Smart Playlist...
2. Complete the Smart Playlist like the screenshot below. Choose your favorite playlist of simply Music. I chose my Purchased music playlist. Click the + button to add the rules. Click OK.
   
3. Type a name for the playlist you just created. I named mine @Shuffle.
4. You need to rate all of your songs (this will enable you to list podcasts first on the shuffle). If you don't feel like rating, just select all songs in the playlist and then choose File > Get Info. Complete the Multiple Item Information box like the screenshot below. Click OK.
5. Connect iPod shuffle. Select the iPod in iTunes Devices panel and click the Contents tab.
6. At the bottom of the window, select the podcast you just created from the Autofill from menu.
7. Click the Autofill button. It may take several minutes to transfer the song files. After transferring the songs, there is still 200 MB of space for podcasts.
8. Click Podcasts in iTunes Source panel. Drag and drop individual episodes you want loaded on iPod shuffle onto the iPod's icon in the Devices panel.
9. Click the iPod's name in the Devices panel. Click the Contents tab.
10. If the My Rating column is not displayed, right-click the Name column and select My Rating. Then, click the My Rating column heading twice. Because podcasts are not rated, they appear first.
11. Disconnect the iPod.
12. Be sure the iPod's Shuffle switch is in the In Order position. To listen to songs, move the Shuffle switch to Shuffle and push the Next button. Sometimes a podcast may get mixed into the shuffle--you'll just have push the Next button to skip it. To return to listening to podcasts, push the iPod's Play button three times in a row. This returns you to the first audio file. If you've already listened to that podcast, push Next until you get to the episode you want to listen to.

So... using iPod shuffle for listening to both music and podcasts is not as simple as we'd like it to be, but it is possible using Smart Playlists and song ratings.