There are 3 podcast hosts that also offer a mobile app that lets you record, edit and publish your episodes. Anchor.fm, Spreaker, and Podbean are making it very easy to record a podcast on your mobile. If you are not using those hosts, you can use a dedicated app to record the audio - Backpack Studio, and then export the files and upload those to your host. You can also improve the sound quality with an external mic that connect into your phone.