If your site is not attached to a group and you want to notify members of new posts and comments, you can install the JetPack plugin.
After activating JetPack, go to Settings>>Discussion..
Once you enable Subscriptions, all members of your site should receive email notifications of new posts and comments.
You can also optionally add a widget that would let non-members subscribe to your site. These will not become members of the site but will be added to a list of emails to are sent out.
Go to Appearance>>Widgets and drag the Blog Subscription (JetPack) widget to a sidebar or other widgetized area. You can customize how it appears on your site: