You can get started blogging by downloading and installing wordpress.
To install wordpress you'll need a web host. I recommend hawkhost web hosting.
They have an auto installer for wordpress which makes it easy to install wordpress.
Next get a domain name. I use dynadot for my domains.
Pick a good theme for your wordpress blog and then start writing great content.
The better the content the more chances you have of getting your blog found in the search engines.
Fill your blog with lots of great content and then apply for Adsense or other Adsense Alternatives such as media.net
Making the money will take awhile and you need lots of traffic to your website first.