I've been trying to figure out exactly how the Democratic Caucus in Iowa works for days, but I can't seem to find any sources that lays it all out entirely. I know that there were thousands of delegates that were chosen yesterday, and that these will vote on a county level and then a congressional district level until 48 national delegates are chosen. The part I'm really confused about is how do the votes in precincts convert into the first round of delegates. But I could really do with a complete explanation about how the entire process works, to be honest.
Several political scientists published a book called "Why Iowa?" which described these processes in depth. Much of the book is available online for free.
Chapter 3 describes "caucus math" and how delegates are assigned based on precinct results. Delegates are assigned proportionally based on the number who caucus for that candidate in each district, with rounding:
If in a group of 200 caucusgoers there are 110 for Obama, 50 for Edwards, and 40 for Clinton once all alignments are made, then Obama will be allocated 55% of that precinct’s county convention delegates, Edwards 25%, and Clinton 20%. (pg.57)
The caucusgoers elect the individual delegates from among themselves.