Step 1: Find a blog host
The simplest way to get started is to use one of the free blog hosting services. Blogger and Wordpress are the easiest to use, but if you are super tech-savvy or design-oriented TypePad and SquareSpace might allow you to express your personality a little better. More here.
Step 2: Determine your goals
Goals don't need to be a formal thing. Simply decide what you'd like to do with your blog. For example, you can focus on one particular class -- a very popular choice -- or write up your guild's accomplishments, detail your RP adventures, compare your alts, or anything you want. Also, think about your audience: do you just want to share your thoughts with your friends or do you want to become one of the WoW power bloggers? More here.
Step 3: Figure out your slant
Since there are a lot of WoW blogs already, you need to decide what you'd like to bring to the party. I originally started my blog with the idea that women gamers might have a different point of view on popular games. However, I found out quickly that instead I preferred simply writing about the shaman class from a beginner's point of view. More here.
Step 4: Become part of the WoW blog community
Read other blogs! Since you're already reading WoW Insider, I'm going to assume you follow at least a few other WoW blogs. Reading these can help spur ideas for you and can help you in other ways. Join Blog Azeroth or Warcraft Bloggers. Get your badge on Entrecard.
Step 5: Write, write, write!
Now, nobody says you must write every day, but try to write a post as often as you can to keep interest levels high. And don't stress about what you're writing. Be casual, be formal, be long, be short, be serious, be funny... but just write!
Updated: We'll be writing a series of more detailed posts on this topic, breaking the steps down further!