There's an exercise program called couch to 5k. Tons of people have used it, it's super easy to follow, and it works.

Download the first week podcast. Pick 3 days and times to exercise this week, 1/2 hour. Follow the program. In 9 weeks you will be able to run 5k.

Its basically music, with instruction to start running, or stop and start walking, over the top.

Theres loads of different podcasts that you can choose that implement it, here's one from the NHS:

https://www.nhs.uk/live-well/exercise/couch-to-5k-week-by-we...

This is how easy week 1 is:

For the runs in Week 1, you will begin with a brisk 5-minute warm-up walk, then you will alternate 60 seconds of running, with 90 seconds of walking, for a total of 20 minutes.

Once you can run 5k, pick a half-marathon 14 or so weeks out. Start a 12/14 week half marathon program. This will usually be 1 weekly 5k run, 1 weekly 20 minute other cardio, 1 weekly ever increasing distance run (5k, 6k, 7k, 8k, 9k, etc.) to the point where you'll run 20k the week before your half marathon.

Then run the half marathon.