1: Go to the podcast listings on your iPad so that you can see the podcast episode you wish to delete.
2: Now swipe your finger horizontally across the episode you wish to delete. When you do, a “Delete” button will be revealed.
3: Tap the “Delete” button to delete that episode. If you change your mind about deleting it, just tap anywhere else on the screen and the “Delete” button will hide itself again without doing anything.
For the Music you will have to do it when the iPad is plugged to your computer.