There is an entire menu section dedicated to comments settings. To access it go to the website admin dashboard and select Settings-> Discussion. This is the place to decide matters such as allowing or disallowing comments on your posts, notifying any website that you might have linked your post to, and all possible comment moderation options.
Default article options
Try to notify blogs you mention in your post
If you select this box, a notification will be sent to the site you linked in your article, appearing in their comment section, if that site allows pingbacks (this means, to receive the notification). The notification is sent when you publish your post.
Get link notifications from other blogs
Conversely, if you check this option, you will allow trackbacks, which are references from other pages to appear in the comments section of your posts.
Allow comments on new articles
This should be checked to give permission for people to comment on your posts. The permission options can also be controlled for individual articles, overriding this general option. If you don’t want to allow comments at all for any post, uncheck this option.
More comment options
The comment author has to include name and email
Choose this setting to make commenters write their name and email. It helps a little with spammers, as they might avoid this extra work.
Registered users only
Select this to allow only registered users to comment on your posts.
Close comments on older articles
Check this box and define a number of days after which it will not be possible to leave comments on the post anymore.
If this is selected, users get a checkbox under the comment area that they can select if they want their name and email to be saved in the browser for the next time they comment.
Allow nested comments
Enable threaded comments, that have a number of levels that you can define (maximum 10) for nested comments.
Break comments pages
Decide whether you want your comments to appear in a specified number (pick how many) of pages, and if you want the last or first page to show first. Within each comments page, you can pick if you the newer or older to appear at the top of it.
Email notification settings
Receive email notifications about comments to your email listed in the General settings menu screen.
Get an email when anyone comments
If you want to be notified every time someone leaves a comment, check this box.
Get an email if a comment is held for moderation
Receive an email every time a comment is being held for moderation.
Approve comments manually
Uncheck this option to approve all comments before they are published.
Moderate comments from previously-approved commenters
Check this only to allow comments to be automatically approved and displayed if they were published by a previously approved commenter (matched by email address). Otherwise, the comment will await moderation.
Moderate comments with links or keywords
You can hold comments for moderation if they include a specified number of links or specific keywords. This is helpful to deal with Spam.
Blacklist comments containing keywords
If you enter some keywords in this box, every time a comment contains the words in its content, name, URL or email, it will be blacklisted, being deleted without warning.
Avatars are the pictures that appear next to the comments. You can choose their settings for your commenters.
Select this option if you would like the commenters avatars to be shown along with their comments.
This is the rating of the avatar you allow to be displayed, in terms of for which audience it is suitable for.
If visitors don’t have an avatar, select one of these options to be displayed based on their email address.