Browse iTunes Store
If you have an internet connection available at your location, you just connect to it and browse iTunes, and select podcast you want to listen to. If you intend to download a music podcast, you have to select it first. A similar process is followed to download podcasts on different issues from other sources directly onto your phone. But make sure the website or download link you are using is safe for downloading and use. It should not cause any security risk.
Downloading Episodes of a Podcast
In case of a music podcast, you might have a number of episodes of it. You can look for one you want to download and click it for the download on the pop-up window. Generally all podcasts are free, but you might be required to sign in or register etc. There are some podcasts, which might require you to pay.
Getting More Episodes
If you are downloading a music podcast, you just need to click on the iPod application on your iPhone and start listening to it straight way. Similar other podcasts can be watched or listened to from your phone. You can access more episode of the same podcast by a similar process.