First you need a platform. This is the place where you create and register your blog. Two of the top platforms are: www.wordpress.com and www.blogger.com.
It takes about 5 minutes to set up your blog, even if you've never done it before. The biggest decision you'll have is what to name your blog, so you can get it registered at the platform of your choice. You will also be able to customize your blog to your liking. A side benefit of having a blog is you can use it to make a few extra bucks. Check out www.google.com/adsense, but don't expect to get rich any time soon:).
You can also check out these two sites: www.squarespace.com, who are offering a new and innovative way to put blogs, and more, online. Another site is: www.LifeScript.com, which offers blogging tips for beginners.
If you need more info about starting a blog, may I suggest you sign-up to ehow.
www.ehow.com is a site where you will find links, articles, and tutorials on this subject, and many others. The sign-up is free.
I hope this answer helps you. Good luck!