They call it pay per click because you only get charged when your ad is clicked on. You dont pay for searches on your keyword rather you only pay when a search has an associated click.
There is another model called CPM (Pay per every 1000 ad impressions) but this model is related to buying advertising on other websites and not keyword based.
There is no flat rate – Google and everyone else wants to get as much money as possible so prices are based on market rates set by bidding with your competitors and also influenced by the quality and relevance of you ads. If your products are specialized enough then you may have very few competitors – this maybe enable you to buy traffic cheap.
You can get an idea of where bidding begins buy using their external keyword tool.
Amit Mehta gives some good tips on how to begin bidding and points out that your CTR is normalized to your ad position . So dont assume that by bidding more google will reward you for a better CTR history because of your ad position – http://www.superaffiliatemindset.com/hot-tips-from-the-ppc-summit-day-2/
You set the maximum you are willing to pay per click and based on the quality of your ads and the relevance of your website to the keyword – your ad is ranked accordingly on the right hand side of search results.
To make sure you don’t spend too much initially, you set a daily budget to limit your expenses while you are evaluating traffic.
Adrian from softwareprojects.com does a great post about pay per click basics and addresses quickly the rules of the game when making money with PPC.