The Twenty Ten theme does support comments. Did you turn on comments in your settings? From the admin dashboard, go to Settings → Discussion and check the box labeled Allow people to post comments on new articles. Check off whatever other options you wish to use.
If you want to turn on comments for your previous posts, go to Posts → All Posts. You’ll see a list of your 25 most recent posts, but because you have so many posts, it will be easier to enable comments for all of them if you display more than 25 posts on a page. Click on the Screen Options tab in the upper right corner, and pick a number like 100 and click the Apply button so that you’ll get 100 posts on your listing page.
Now, check the box next to the word Title. This will check all of the posts on that page. On the Bulk Actions drop-down, select Edit and click the Apply button. A section will then open up.
On the Comments drop-down, select Allow then click the Update button. Comments will now be allowed for all of the posts on that page. Click to the next page of posts and repeat the above steps.
One final suggestion: the default WordPress commenting is prone to spamming. You may want to consider a service that requires users to be registered before commenting. I like Disqus because it’s fairly widely used. It’s easy to install, just go to Plugins → Add New and enter Disqus in the search field (although you will have to register for your own free account; the plugin will show you a link once it’s installed).
