Some people frown upon it, but using adwords and bidding low, hoping a user will come and click on one of your higher paying ads, is allowed per TOS. (i.e. there is nothing saying you can't) And it works. You will most likely at least break even but if you have good content you will get return visitors and they'll tell two friends, and they'll tell two friends and so on and then you won't need ad words anymore.
There is a lot of good advice to be had here at webmasterworld. Read old threads, and ask more questions.
Definitely place adwords on inexpensive keywords. It even works well to be the last ad on a competitive keyword, as long as your clickthru rate is high enough that Google doesn't disable your ads. You never want to spend a lot of money on an adword click unless you're in a real hurry to make a lot of money from the person that clicks.
The way you want to advertise is in such a way that those who click the ads you place are likely to give you links. Ultimately it is these links that will lead the search engines to refer a lot of free traffic to your site. Don't try to advertise in such a way that those who click the ads you place will click the ads you publish on your site, because the money you earn from their click won't be worth as much as a link would have been.