Most people get money from blogging by selling adspace on their website, or to sell their own goods and services because the blog draws in more customers.
There's one other way, which is what I do: ghostwriting blogs for other people.
Say someone has a business restoring antiques and they sell them on their website. A blog about home decorating can draw in a lot more traffic so people will see their wares for sale, but they can't write very well. So they pay me to write it for them.