There are lots of ways to earn money with your blog. And the most common these days is with ads. How do we earn with ads? It's very simple you register to ad serving companies and they will find advertisers for you. And when the ads will be shown on your page you will earn money fro the number of visitors and clicks on the ads.
The most used advertising firms are adsense, chitika, infolinks, adbrite and many more, you can do a research for your own and select what's best for your blog topic.
Another way is by affiliate marketing. This is done by placing product links on your blog and when someone buy there or register with that website you will receive commission. These products are mostly online shops or web services so that it will blend being placed on blogs.
There are also two kinds of ads. Direct and indirect. Direct ads are you will contact or search for advertisers and do not need to use advertising companies to find advertisers for you so will receive the full payment from the advertisers. While indirect ads are those what i said about in the first paragraph. You will get 60-75 percent only of the payment given by the advertisers and the advertising company will get the remaining earnings.