Each mp3 player will be different but, basically, you need to plug your player into your computer (usually via a USB cable) so that it appears as an external device. Simply locate the podcasts episodes which you have already downloaded on your computer, and then 'drag and drop' them onto your MP3 player. Once the files have transferred, you will be able to disconnect the mp3 player and listen to the podcast episodes on the move.
Fortunately, some mp3 players also come with software to allow you to "sync" the podcasts you have subscribed to on your computer with your player. This means that each time you plug in your mp3 player, the software will automatically transfer the latest episodes of your chosen podcasts to it. How this works depends on the brand of your mp3 player and the software you are using.
If this did not answer your question, please advise what information you would expect to be provided.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.