However, before you do that, please be aware that the new Blogger Beta offers the ability to add "categories" to your blog, in the form of "labels"...
Using the labeling system is a much easier method of adding and maintaining categories on your blog, and the new Blogger Beta offers other advantages as well. However, you must be willing to migrate your template from the old Blogger platform to the new Blogger Beta platform. This will involve some work, but as I understand it, in the future all Blogger blogs will be switched to the new Blogger Beta anyway (so might as well do it now)!
Here's what you must do to switch to Blogger Beta then add Labels/Categories to your posts:
1. Get a Google account, if you don't already have one. If you have Gmail, you will already have a Google account (Note: you must be invited by someone who has Gmail in order get Gmail, or use one of the methods describe in this article). If you need an invitation and don't have any friends in the world with Gmail, I'll invite you...just kidding, I can send you an invitation if you really need one).
2. Once you have your Google or Gmail account, switch your blog and the template over to the new Blogger Beta, following the instructions on this page. [NOTE: It may take you a while to update the template, if your blog had many customizations and you want to keep them. I took switching over to Blogger Beta as an opportunity to give a fresh new look to my blog, as I updated to a three-column template that I find much more useful. Once on the Blogger Beta platform, layout changes are much easier, as you can drag elements where you want to put them. Also these changes are instantly updated, unlike on the old Blogger where pages must be re-published and can take a long time to do so. In any case, once your template is updated to Blogger Beta, you will be able to use the labels feature to create and easily maintain categories for all your previous posts].
3. Decide what labels (categories) you want to give your posts.
4. Log in to Blogger Beta, using your Google/Gmail account and go the dashboard. Click on "Posts".
5. Click on "Published" to see all your published posts. Now you can add a label to each post, or to multiple posts at the same time.
6. Click the "Label Actions" drop-down box, click on "new label", and type the name of your label. Then apply the label to whichever posts you want by clicking the box next to the post title(s).
7. Once you have labeled all your posts, you must then add the Labels "widget" to your blog. This will create a Labels sidebar in your blog. Go to the Template screen. Click on "Add a Page Element". Choose "Labels". Select whether you want the labels to appear in alphabetical order or in order of frequency. Also you can give whatever title you want to the sidebar (you don't have to call it "Labels").
Now if you would like a fancier version of labels, there are ingenious Blogger Beta hacks out there, such as the one for Multi-Style Labels widget by Hackosphere that I'm currently using. Also, check out my new resources section, Blogger Beta Hack Creators, to find links to the blogs of the talented people creating these hacks.