How can I sync Apple Podcasts from iPhone to Apple Watch?

I am having endless problems getting podcasts from my phone to my watch. The podcasts start downloading, the orange circle gets halfway or three quarters of the way through, and then starts spinning again and we're back to square one. The phone says waiting, and it waits forever. This more or less defeats the purpose of having a watch, since I want to use it for exercise, rather than carry my phone.

Can anyone help? Or recommend a good 3rd party app? This is insanely frustrating.

[Re-Titled by Moderator]