First, go to this page. This is what you'll see:

Your first task is to set up your own account. Please use some recognizable version of your name so that we can get back to you directly if necessary. To set up your own account, click on the "Open a new Bugzilla account" link. That will take you to a page that asks for your email address. Just type it in and we will forward it to a consortium of Russian spammers who pay us $0.001 for each name...
No, just kidding... enter your email address and it will send you an email with instructions for creating your own account. (Warning: there's a chance that your ISP or email program will think it's spam, so be on the lookout for it!) Follow those instructions and you'll be set up with an account.
Once you have your account, you can login with your email address and password. It will set you up with a cookie so you never have to worry about it again. Once you have logged in you will see a window looking like this:

You might want to read the "Bugzilla User's Guide", but that's not really necessary. Your major interest is in clicking on the "Enter a new bug report". That will give you a window looking like this:

You should definitely read the "bug writing guidelines". You should also look at the "most frequently reported bugs" to make certain that the bug you're reporting hasn't already been reported. However, if you do manage to report a bug that has already been reported, you won't burn forever in Storytron Hell. You'll just spend a little time in Storytron Purgatory.
The important data to enter are the Severity, the Summary, and the Description. The Severity is your guess as to how serious the bug is. Select a rating from the pop-up menu.
The Summary is a short description of the bug. Try to capture the essense of the problem in ten or twenty words. Summaries that say "Swat screws up" aren't very useful. It should be something as specific as "Script display shows wrong color for BQuotient Operator".
The real work is writing up the Description. The most important element of the Description is a statement specifying exactly how to replicate the bug. If you do a good job here, then it will be easy for us to figure out what's wrong and how to fix it. The kind of Description that WILL get you sent to Storytron Hell doesn't clearly show how to replicate the bug.
Here are two examples of how to report the same bug; the first is the wrong way and the second is the right way:
WRONG:
"Nothing happens when I add a new Custom Trait."
RIGHT:
"Launch with BoP2K and bring up Custom Traits Lizard. Add a new custom
trait by entering text in the empty trait box but don't hit ENTER. That
trait now appears to be part of the Custom Trait list, but consulting
Actor Editor demonstrates that it has not yet been included."
Yes, it takes more work to right it properly. But if you don't explain the bug in a manner that we can reproduce, you're wasting your time. Besides, think of all those innocent electrons whose lives will be wasted storing and communicating your useless bug report!
Another consideration is the storyworld on which you report the bug. It's best if you can reproduce the bug in one of the standard storyworlds that is freely available to all, such as ChitChat. However, if the bug only appears in your own storyworld, then you'll have to send us your storyworld. You can do that by using the button that says "Add an attachment". Just attach your storyworld there.
When you've got it right, hit the "Commit" button and the bug report is saved. Bugzilla will immediately send emails to all the programmers announcing this new problem. Sometimes we can fix the bug in minutes. Sometimes we'll just snort and laugh.
OK, so now you're all set and ready to download Swat!