First is to enable the Comment module, which you should already have done. In the User Management area is the Permissions screen which has a section for comment permissions:-
- comment module
- access comments
- administer comments
- post comments
- post comments without approval
Access comments controls which set of users are allowed to view the comments. Normally you want all roles to access comments.
Administer comments controls which set of users can edit or delete all comments, plus it controls access to the Comments administration screen. This permission should be confined to specially selected moderators.
Post comments and Post comments without approval control which set of users can, uh, post comments. The "without approval" means that such users can post a comment without it being held for approval. Comments can be 'unpublished' meaning that they aren't normally visible, except that moderators can see the unpublished comments. Moderators can then edit the comment and make it published, thereby making it visible to the public.
The permissions for posting comments have a big effect on whether your site builds up any community, or not. A rich discussion through the comment system can build community and interaction.
However the comment system can also be a spammer magnet and there are spammers with software that knows how to automagically spew spam comments into a drupal site.
There are some additional (contributed) modules which can improve the behavior of comments:-
Comment notify allows you to subscribe to a given node and receive emails when comments are made.
Comment redirect fixes a misbehavior if there are lots of comments on a given node. Drupal doesn't handle that situation very well, and this module fixes the situation. It's also noted that a more comprehensive solution is being developed for Drupal 7.
Notifications is another way to be notified of comments. Not just comments but a whole lot more. Also Notify and also Subscriptions and also Watcher
Quote makes for a nice experience of posting a reply comment and automatically quoting text from the comment you're replying to.
Re: Comment subject automatically generates a "Re: xyzzy" comment subject.
Signatures for Forums improves the experience of having a user controlled automatic signature pasted into the end of their postings and comments.