If you click this link, you will go to the comment posting page. (Note: in some templates, this link may take you to the post page first. From there you should be able to find the "Post a Comment" link which will take you here.) The comment posting page looks like this:
In the upper left corner, there is an option to show or hide the original blog post that the comments relate to. The rest of the left-hand column contains any comments that have already been made. The profile photos of the comment authors may also display, depending on the blog's settings.
On the right hand side of the page is the space for you to enter your comment. Beneath that are the identity options. (Some of these may not be available, depending on the blog's settings.)
The options are these:
Blogger username: Your display name will appear, along with a link to your profile and your photo (if you have one).
Other: You can enter your name and a link to your website, without having to have a Blogger account.
Anonymous: No identifying information is displayed. The comment is credited to "Anonymous" without a link.
The owner of a blog also has the option to have comments open in popup windows. In this case, all the primary features will still be present, just arranged a little differently: