How do I get on a podcast to promote my product?

Short answer

By pitching a topic, never a product. Hosts need an interesting episode; nobody books a guest to hear about a piece of software. Find shows whose audience overlaps yours, listen to two episodes so the pitch is specific, and offer one genuinely interesting story you can tell — the technical problem you solved, the thing you got wrong, the counter-intuitive finding from your data. Small shows convert better than big ones and are far easier to get on.