How do I attract businesses to purchase banner ads on my site?
You should think of the advertiser as your customer, and your website as your product. You need to package information about your website in a way that appeals to an advertiser. Particularly, you need to quantify your audience--visitors, page views, loyalty, demographics.
If you've got a good audience within a clear niche, you could simply approach potential advertisers that you think are relevant to your audience. Most banner advertising is based on CPM (cost per thousand impressions)--the value ranges depending on how desirable your audience is.
If you don't have a lot of visitors, or a particular niche--and even if you do--then advertising networks (like Google Adsense) are a great, and simple way to get going.
The network takes care of finding advertisers, charging them and paying you. Of course, they make a profit while doing so--some of the advertising revenue goes to the network. Affiliate networks (like Commission Junction) will let you choose which advertisers you show, and you'll earn money when your site visitors complete a purchase after clicking on your ads.