There are a variety of different exchange plans, but most (virtually all) are based on the exchange plan first developed for diabetics in the late 40's or 50's by the American Diabetes Association and the American Dietetics Association.
The exchanges themselves haven't changed much, which makes it nice, because almost all exchange plan cookbooks can be used by almost every other exchange plan.
In most exchange plans, there are 6 exchange categories.
Listing the exchanges and their approximate calorie count
Protein or Meat (55)
Fat (45 calories)
Veggie (25 calories)
Fruit (70 calories)
Milk or Dairy (90 calories)
Starch or Bread (80 calories)
How many exchanges you get from each category depends on the exchange plan you choose (I've linked some examples).
There are books and online exchange counting resources, so just as with "straight" you can look up exchanges online or you can buy exchange list books. You can also learn to calculate exchanges by using the nutrition label (instructions are online, and also in the book Exchanges For All Occasions, 4th edition (I've read that the 5th edition does not have this information, but I don't know about the other editions).
I don't know if I'm explaining it very well, so you may find these link easier to understand
Introduction to Exchange Plans (great overview)
http://frugalabundance.com/frugal_fa...hange-plan.htm
Examples of exchange plans.
http://frugalabundance.com/frugal_fa...food-plans.htm
You can also find other helpful information on this site, so here's the index page where you can find food lists and even food journal pages (which give you room to write what you ate, but also a chart to check off each exchange as you eat it).
http://frugalabundance.com/frugal_fat_loss/index.htm