Tumblr does not, strictly speaking, have a comment system -- if you want to add your two cents to a discussion, you almost always have to reblog the post. There are only two exceptions to this, both requiring specific sets of circumstances. Both appear in the "Notes" section of a post, alongside the reblog icon. Tumblr calls one type of comment "replies" and the other "answers."
For you to be able to add a reply to a post, the owner of the blog it appears in must have activated the feature. Depending on its settings, you can reply if you've been following that blog for longer than two weeks or if the blog's owner is following you. You can only add a reply from your dashboard. You are limited to a maximum of 250 characters, and you can only add one reply to each post. You can't reply to your own posts. You'll know you can reply to a post when you see a speech bubble icon on it.
Question posts have an additional text field directly beneath their contents, both when you view them from your dashboard and when you open the individual post page. As long as you're logged in to Tumblr, you can answer a question post either from your dashboard or from the individual post page -- even if you're not following the author and she's not following you. Answers are limited to 140 characters.