Out of the box, Drupal 6.x is not configured to notify anyone when a new comment is awaiting approval. If you have decided to require approval for all new comments, you can do one of two things:

1. You can visit your site on a regular basis to check for new comments awaiting approval, OR
2. You can configure Drupal to send you an email whenever a new comment is created.

I prefer #2, so let's see how that works...

First you need to create a new action.
Go to Administer - Configuration - Actions. Make a new advanced action based on Send e-mail...

Configure the new action to send you (or your site administrator) an email.

Then you need to assign a trigger to the action you just created.
Go to Administer - Building - Triggers. On the Comments tab, assign the new action to the trigger After saving a new comment.

Now it just needs to be tested.
Log out and then add a new comment somewhere on your site. Then check your email and you should see the new notification.