You should then be looking at a basic front page which gives you several options, the most important of which are probably "Query existing bug reports" and "Enter a new bug report", each conveniently placed near the top. Alternatively, if you know the bug number that you're interested in, you can enter that in the text entry field and hit "show" (or on most pages, enter it in the text entry field in the light yellow section at the bottom).
First off, though, you probably want to create an account. Select "Open a new Bugzilla account", fill in your details in the form and hit "Create Account". You'll receive an e-mail with your Bugzilla password which you can then use to log in.
When you log in with your new account, you'll get a bug search form that you can use to search the database for bugs. But first, you probably want to change your randomly-generated password to something you will remember. To do this, click on the "prefs" link in the light yellow section at the bottom (or use the link in the e-mail you were sent), and this will take you to a page where you can perform account maintenance, including changing your password (Account settings), watch another user if they're away and select when you receive e-mail (Email settings), do some (very) basic customisation (Page footer) and check what permissions you have (Permissions).
OK, let's file a new bug. Click on "New" in that yellow section at the bottom, and then select the particular product. If you aren't sure which product you should select, or you don't see the product you're want to select, e-mail Gene. You should then be able to enter the bug. Select the version, component, platform, operating system, priority and severity. You probably don't want to touch the "Assign to" field --- Bugzilla will assign it automatically to the component owner (there's no way of getting, say, a drop-down list of people with Bugzilla accounts, so it's probably best just to leave this field alone). Enter a brief summary, and a description of the bug, being sure to include all relevant details. Finally, hit "Commit" and Bugzilla will add it to the database.
You can then add additional comments (things you forgot) or attach a file (such as code that will reproduce the bug) and hit "commit". Actually, this is pretty much the same page you'll get when you're looking at any bug that you're permitted to modify. Down towards the bottom (just before the "Commit" button), there's a set of radio buttons that change the status of the bug. You can accept the bug (agree that it's a problem and that someone's looking at it); resolve the bug with one of several different resolutions such as "fixed", "wontfix", or "worksforme"; resolve it as a duplicate bug, or reassign the bug to someone else. Someone with sufficient privelege needs to close the bug once it's been resolved.
You can see which bugs have been assigned to you by clicking on "My Bugs" in the light yellow section at the bottom (you should also have received an e-mail when you were assigned).
Lastly, you can search the bug database. Just click on the "Query" link in that light yellow section at the bottom and you will get a form which looks to be pretty intimidating. But it's not, really. Just fill in whatever you're interested in, and hit "Search". For example, you can get all PSLib Priority 1 bugs that have been resolved with a resolution of "fixed" in the last 2 weeks. You'll get a page with a summary of each of the bugs meeting your search criteria, and you can then click on the bug number to view the bug, add comments, resolve, etc.