What's your level of fitness? I do recommend going to an rkc, saying hi, and learning how to properly swing (dragondoor.com). That's the russian hard-style technique. It's worth it just to go and learn how to do it without ripping your shoulder blades to shreds or killing your back.
I know when I first started out I had issues doing more than 30 swings a session w/ a 35lb bell.
If you buy Pavel Tsatsouline's book Enter the Kettlebell, he recommends doing a 12 minute session with as many swings as possible broken up with periods of light jogging to keep the heart rate reasonable. So in that, I can do about 160 swings, which is about the minimum I'm doing these days.
Generally I'll switch between my 35lb and 53lb kettlebell and do 150-300 swings in a 30 minute session 2-3 times a week. That and turkish getups, pushups and other bodyweight exercises are all I need right now. I've lost over 30 pounds with my current paleo diet and kettlebell swings (and I haven't stepped on a treadmill once!). I'm going to keep doing it as long as I see results!
There is a lot of different types of swings you can do,
Russian Swing (Chest High)-- American Swing (Over head)-- Power Swing (chest high, but stopping the kettlebell and pulling it down, much more effort involved in grip and cardio)-- Turkish Get ups (Builds excellent shoulder stability)-- Floor Presses-- Shoulder Press-- Bottom Up shoulder press-- Push Press-- Single Arm swings-- Holding the kettlebell by the bottom (grip test)-- KettleBell cleans-- KettleBell Snatches--
As for an amount have fun mix it up, try different things, learn new skills, swing with your eyes closed, alternate hands, around the legs. Mid air flips...
Most importantly keep in mind, if you drop it fast feet are happy feet.
I would never do a set number of swings every day, good lord I would be bored out of my mind. Alternate there is so much to do with a kettle bell you could come up with some kind of weekly routine and rotate it, or go for a time domain like as many swings as you can do in 5 min with the various types of swings. Heavy days, lights days, skills days.
I do not know what you really want to hear for an answer, if I had to pick a number I would say mix it up... High, low, medium, skill days, strength days.
Take your time learn the movements, and have fun. You can learn a lot with a kettlebell that will have other people looking on with amazement.
Check out the store, I do not have the DVD's but I have taken the course, I learned a lot and have used a lot of it in my training.
You should not be doing KB swings exclusively. There are a wide range of crossfit-style workouts that involve the KB that will work out your body in many different ways. I would think this would be different depending on the individual/weight of the KB.
I am a 180lb, male 5"10 and I use 1.5 pood, so I would probably do 100 and then do some Turkish Getups or something.
Why would you only do KBS(KettleBell Swings)? If you'd like to get fit, varied exercise is rather important. Kettlebells are amazing things, but there's a lot more out there! Get running, swimming, cycling, weightlifting, gymnastics etc. etc. :)
Anyway, if I would do only KBS, I wouldn't do a set amount. I would rather do tabata's (20 sec. work, 10 sec. rest and that 8 times, the lowest amount of reps is your score (so keep consistent)) or make small workouts of 5-10 mins, trying to get as many reps as possible while maintaining good technique of course. Like Ryan H said here above, there's a lot of different movements you can do with KettleBells. So also try varying different movements. But keep it short so intensity is high, in my opinion :)
To echo what some others have said, why are you only doing swings? Learn to snatch, clean&jerk, and press.
These days I have about 4 different kbell workouts: heavy variety, medium snatch, light VO2max snatch, and strength pressing.
Lots of other stuff also.