Eurail:
http://www.eurail.com/
Eurail tutorial:
http://www.ricksteves.com/rail/
The tutorial is decent, but it has one big flaw: I compares only normal fare train prices with the price of the Eurail pass. It does not compare special offers, bus tickets or plane tickets nor gives it any hint that these are alternative options.
Budget: You should plan on having at least 50 EUR per day and person, but 65 EUR per day and person would be better. That is just enough for hostel beds and food from the supermarket though, so if you want hotels and dining out plan on 120 EUR per day and above.
Airfare: around 600-1000 USD roundtrip including taxes from a major airport in the USA (New York, LA, Miami, Chicago, ...) to one of the hubs in Europe (London, Frankfurt, Paris, Rome).