When writing a blog for someone else, you generally don't make it personal like you would your own blog. You can write the blog like an article but with a more casual tone that sounds like you are talking to a friend. The information has to be interesting, helpful in some way and correct just like an article, but the writing style can be less formal and more fun.
There are a few ways to find paying jobs for blogging. At Constant-Content they accept blogs for sale on just about every subject. Make sure to read a few there first, as well as their writer guidelines before submitting material. You can also bid for jobs on blogging at Writerlance.com but don't expect the pay to be too high. Writerlance is a free service but you do have to join to use it. Craigslist.com, the ODesk and GetAFreelancer.com are all writing sites where you can look for jobs online as a blogger. Do a little digging and you are sure to find some great blogging jobs online.
For the more accomplished blogger you may want to apply at About.com. This site actually hires writer and pays a good salary for you to create and continually update a blog of a specific subject. They generally have the subjects they are in need of posted so you can apply for a specific topic.
There are sites like Hubpages, E-How and Xomba where you can create a blog page and earn money by using either Google Adsense or from clicks on your articles. These generally don't make too much money unless you have a lot of followers. They are, however, great places to show off your writing skills if you need a few clips for writing jobs you apply for. So if you are a beginner blogger, you may want to try these out.
Blogging is fun and profitable, especially if you can blog for someone else. Sites are always in need of new material to keep their blogs fresh and updated, so there will always be work in the blogging field. If you are good at blogging, and enjoy it, then this may be the right writing job for you.
Let me know if you try any of these suggestions or if you do write for blogs. Would love to hear from all of you.