I have seen many references to Amtrak being less expensive then flying. I have a family of 2 adults and three kids, and I've priced out trips from our home station of Houston to a variety of locations, and most are much more expensive or very close to the same as airfare for the same trip.
What is the secret to making train travel more affordable than plane travel? Any tips from experienced train travelers?
To split your question, the secret to making train travel more affordable is to live near a major city on the east coast.
The secret to making it more affordable than advance-purchase airfare for long-distrance travel simply doesn't exist.
AmTrak works best for short regional trips between cities, especially cities on the east coast. Also, for the most part, a last-minute trip by train is going to cost less than a comparable last-minute trip by air, but it still won't normally be *cheap* by any means.
Add in the lost income and additional food costs that come out of adding on travel days, and US train travel is almost never less expensive than traveling by air, provided that you were able to plan the trip at least 30 days in advance.
That said, I love travelling by train, and I use it whereever possible when in Europe or traveling between cities on the East coast. For shorter trips it is sometimes worth it to me to pay more for a train, because it can be more convenient as long as I'm traveling on a dedicated rail corridor.
PS: As an example, I just priced a trip from Alexandria, VA (outside DC) to NYC-Penn Station on April 5th. Amtrak happens to have a special that day, so the fare is $66 (the most expensive fare that week on this route is $135). Airfare on the same route (National to LaGuardia, to minimize ground transportation costs) is no less than $177 that day, and that is before taxes and fees, which are much higher on airfare.
For fun, I also priced Houston to Dallas, tomorrow. On Amtrak that is $63 (but takes nearly 9 hours), while by air, the same trip (from Hobby to Love) is $163 (but takes one hour). However, if I price the same trip for April 27th, the train is still $63, but the plane is $49. See what I mean?