Recording
Most of these recordings were made with an iPod (either a 5th gen. video iPod, or 2nd generation iPod nano) and a Griffin iTalk Pro microphone. These sit right on the table in front of the musicians. Amazingly, this setup can pick up the music well even at sessions where the musicians themselves have a lot of trouble hearing the music because of the noise of the crowd.
When recording with the iPod, you can hold down the button on the microphone to bring up a menu that lets you record in one of three settings: "Low Gain", "High Gain", and "Automatic". The automatic setting switches back and forth between low and high, depending on the sound level -- I have found that it works very poorly. To avoid clipping, I set the mike to "Low Gain". The noise level is very low (it isn't plugged into the wall at all), so I can increase the volume of the tracks later without introducing a lot of noise.
In order to get good results and not have the recording skip every few seconds (due to hard disk access issues on the iPod), you need to have your iPod nearly empty, and have it set to not import any album artwork. The battery will record between 1 and 2 hours on a full charge, depending on how old and abused your iPod battery is.
As the iPods and microphone I have been using are no longer being made, I have switched to a very nice and reasonably priced field recorder, the Zoom H2. Initial results with this recorder have been outstanding. If you're planning to record more than 2 hours, make sure to bring extra batteries though :) With the Zoom H2, I use the medium gain setting and the 2 channel surround setting (so that both front and back microphones are active).
Post-Processing
I don't do much, other than selecting out the exact part of the recording I want, and adjusting the volume level of the track. Typically I have to increase the sound amplitude by a factor of 3 or 4, because of the low gain setting of the microphone.
With Zoom H2 recordings, typically the two channels are not equal in loudness, so I amplify them separately to get them up to equal volume.
With iPod recordings, the recordings are copied onto your computer as WAV files called "Voice Memos" when you sync your iPod. If you are using a Nano, they will not be WAV files, but AAC lossless files and will need to be converted. Most sound processing programs can read those files and manipulate them. I use a command line utility called SoX, known as the "Swiss army knife" of sound processing tools. It is not very user friendly, but is free and does what I want very well. Another very good utility that I've used for doing simple sound manipulation is Audacity; it is also free and open source, but much more user-friendly and better documented.
After I get the track I want, I use either iTunes, Audacity, or the LAME program to encode the track as an MP3.