When I used to change up my blog design often, I was asked this question a lot. Not so much anymore. But it's still good stuff to be familiar with, so I'll gladly pass along what little I know to the few people still reading this defunct log of family events. :D
Here's a list of things I did in order to become semi-proficient at tweaking my blog html:
1. Create a new practice blog that exactly mirrors your working blog. Any time you want to make a new change, try it out on the practice blog first so that you can be sure it will turn out just how you want it before taking the plunge on your public blog. This step will save a lot of heartache. Believe me. I learned this valuable lesson the hard way.
2. Take it one step at a time! There is so much blog personalization html floating around out there on the world wide web. It would be easy to get overwhelmed and confused. Just pick one thing you'd like to see on your blog (i.e. flash header, tabbed sidebar menu, large photos, etc.), and work on that first. Then move on to the next when you've perfected that tweak.
3. Research. A lot. Check a whole bunch of different how-to links before you decide on which method to follow. There tend to be multiple ways to arrive at the same result, so read a bit before you settle. Read comments on blog posts to take note of any bugs that people have encountered after following directions. Check post dates to see if something is outdated. Better yet, search with a date in your search field to get the most recent posts.
4. Ask. Sometimes you'll come across a blog that has an awesome widget/header/background/layout, and all you have to do is ask the blog owner exactly how they came by it. People are often more than happy to share.
5. Right click on an envied blog and select "view page source" to see how that blog is configured. I have learned much about html this way.
6. Play! Play with your html. Play, play, play. Especially on your practice blog. Tweak one thing at a time to see exactly which codes will change which items on your page and how they do so. As nerdy as it sounds, it's actually fairly empowering to be somewhat familiar with html. I guess it makes sense seeing as how knowledge = power. Right? :D
Hope this helps all you budding bloggers out there. Enjoy your space on the Internet. Personalize it. Perfect it. Making it your own will encourage you to frequent it more often.