When you say "download," do you mean downloading podcasts to your Mac, or loading (syncing) podcasts on your iPod?
Since this is the forum calegory for "Older iPods," I'll go with syncing podcasts from iTunes library to iPod...
If you are using automatic syncing to load other content, such as songs, you need to set up the iPod's Podcasts tab in iTunes.
(If you have been using the manual method to load content on the iPod, please post back.)
Select the iPod in iTunes. There is a bar of "tabs" (starting with Summary). Click on Podcasts there. This is the Podcasts tab, where you tell iTunes how to sync podcasts to your iPod.
Sync Podcasts is checkmarked. If you want to automate selection of podcast episodes for syncing, check the box for Automatically include [option] episodes of [option], and set the options as desired. NOTE: If the first option includes the word "unplayed," iTunes automatically removes played podcast episodes during the next sync.
Set up the rest of the Podcasts tab, as needed and desired. When you click Apply, your selections on the Podcasts tab, and other tabs such as Music, are loaded on the iPod, replacing its existing content. Going forward, any changes to the iTunes library related to the sync settings on the Podcasts tab (and other tabs) sync automatically when you connect the iPod or when you click the Sync button.