The savings are worth the 30 GBP if you’re doing a few train trips, including the Heathrow Express. But buying this online is NOT an intuitive process, and you CANNOT purchase the card at Heathrow Airport. I wrote to Railcard Help and got a reply two business days later (plus a weekend).
On the US passport, look at the very bottom and you’ll see a long string of numbers that begins with your ten digit passport number. Enter those 10 digits, followed by USA, the next 7 digits, followed by F or M for your gender. And here’s the tricky part. Enter the next 7 digits, and then skip to the very end, and enter the LAST 2 digits on your passport code. For non-US passports, the process is the same, except that your 3-digit country code will be different, and you may have to enter chevrons, instead of numbers.
Make sure to enter your full name exactly as it appears on the passport.
Good luck!