You could write a bible-sized book entitled, How To Make Money With Online Advertising and still not scratch the surface. Everyone from a high school kid making t-shirts in his parents' territory on up to the largest corporations in the country can make money with online advertising.
There are a myriad of methods to make money with online advertising, but the most popular is using Google AdWords. Each search engine has its own version of this, but since Google is by far the most popular, I'll concentrate on AdWords.
Whenever you make a search in Google, the results you see at the very top in the shipped region and all those little ads on the right hand side are paid advertisements. Whatever you typed in the search box to get to that search result is called the "keyword". A keyword can be one or many words, so it can be a little confusing.
What the advertisers do is bid on the different keywords so that their ads are shown closer to the top of the search result. Each time someone clicks on an ad, the company is charged whatever that bid amount is. This is called PPC or Pay-Per-Click. It's pretty ingenious because companies only pay for advertising that is being used.
PPC is like putting up a billboard on the side of the highway and only being charged for each driver who actually read it. For those who just glance up with no interest, there is no charge.
Obviously, there is a science to effectively using Google AdWords and you can lose a ton of money if you do not know what you're doing. So, if you are serious about using it, either get a good book or find someone who can teach it to you. If you know how to use AdWords, there is no quick way to take your online business to the next level.