First, you'll need to find a theme you like. I listed a few places to get free themes HERE. If there isn't one on the sites listed in that post, you can Google "Free Blogger Themes" or "Free Blogger Templates".
Once you've found the theme you want to put on your blog, you should see something like this:
You can click"Live Demo" to see what it looks like full size. Click "Download" to download it. Make sure you put it somewhere you can find it and DO NOT OPEN IT.
Now, go into your Blogger Dashboard, click "Design", click on "Edit HTML" and you'll see this:
Don't mess around with all the jibber jabber HTML code, or you will do some damage unless you know what you're doing. What you need to do click on "Choose File". Select the template you've downloaded and click "Upload".
Make sure you save your changes. Always save your changes. Now you should be able to see your new template on your blog! Once it's on there, you can work on placing your widgets where you want them and getting your new blog (or newly made over blog) ready for the public to see.