You don't need tickets for any of the Eat to the Beat concertsthey are free with park admissionbut you may want to line up early to get a good spot.
You pay as you go for the food booths set up around World Showcase. Each booth takes cash, credit cards,
Disney Dining Plan snack credits (well, they have in previous years), or Disney gift cards. The food booths are only one aspect of the festival, thoughthey also have special "hard ticket" events like the Party for the Senses and the weekly dessert parties, plus seminars and cooking demonstrations, chef/author meet-n-greets, etc.
This page offers a great overview of last year's event so you can get a feel for what all is involved:
http://www.wdwinfo.com/wdwinfo/guides/epcot/events/