The economics can be pretty bad, a lot of people don't make much money but they also don't make quality games or read the market. There are success stories, Hero Interactive, Berzerk Studio, Nitrome, Armor Games, Long Animals etc.
You should check out http://www.flashgamelicense.com/ it's a site where developers sell the sponsorship rights for their games. The guys who run it are very helpful and there's a forum full of information and a chatroom where you can usually find me and a bunch of other people trolling away.
In a nutshell: Mochi and CPMStar offer ads to go in the games. Mochi's CPM is usually pretty awful (I've served 6m+ ads for a lousy grand), CPMStar generally pays more but is more exclusive, it's harder to get them in your game.
GamerSafe (run by the FGL guys) and Mochi both have virtual goods/transactions platforms to charge for stuff in your game, I haven't used either yet.
Sponsorship is usually going to be the major source of revenue. Kongregate, Armor, Addicting etc pay for the branding rights in your game (the splash screens etc). This can go high into the 5 digits if you're talented enough - there are guys pulling 6 digits a year off this stuff, a couple that might be inching close to 7, and a lot that make between $0 and bugger all.
Andy Moore who was the community manager for Fantastic Contraption and then went on to make games himself has an awesome writeup about his game Steambirds:
http://www.andymoore.ca/2010/03/steambirds-by-the-numbers/
Chris Gregorio (xdragonx10) who makes the Medieval Rampage games amongst others has a great breakdown of his earnings and strategy here:
how do we save posts in HN?
1. In game ads. When I was at MochiMedia, the top game developers earned around $10k/month, so it is possible. That said, there were only a handful that were able to do that well. Most people made far less. Even games that you would consider very successful made around $200-$400/month. The money to developers is around a $0.25 CPM. That means to make $250 in a month you need 1MM game plays.
2. Virtual Goods. Since I left Mochi, they started their MochiCoins program where developers can sell virtual goods directly to game players. I don't know the official numbers, but I heard the successful guys were doing as much as $1k/day. Again, that's the top end and most people were far lower. The bar is much higher in creating a good game here as you're going to try and get a user to actually pay for it.
If you do know how to make fun games, it's possible to make money with determination using an ad supported site and games. Small, free games are a good way to build up traffic to your site, and also a good way to learn what kind of games will find an audience.
Ultimately though, for a successful game with a decent amount of depth, you'll make so much more money charging players that it'll be crazy to keep them free. At least 10x more per visitor if you at some point ask for money.
Some background on who you are and why you're asking would be helpful in giving a more detailed answer!
I think it goes like this, very generally: 1. Free game w/ licensing + ads 2. For-sale game (backed up with free version for distribution) 3. Persistantly free game w/ usual freemium hooks
You can make more as you go further down, but there's also a lot more work involved.
The success curve for this looks a lot less intimidating than the success curve for game development generally. (Which is even more painful than the success curve for "selling software on the Internet", which is already pretty brutal.)
Flash games are already a big gamble of time and resources, with the odds of a decent return getting worse. Our shop bailed out over a year ago and don't regret it.
Still focus on flash, as it is not going any where any time soon, but also diversify your funds. If you make a flash game try to also port it to html5 so that you can reach the Android/Apple iP(ad)hone market, and if you can't... don't sweat it.