How do I use Areas and Iterations?

I don't know what do do with them.  Can I get away without using them?  It's just one more thing to fill out for each work item. 

You could.  After a few years of tracking projects with Team System, you'd probably regret it even if you're a one person shop.  Areas and iterations are intended to be used for product and time categorization. They're a tree structure, so if you set them up right you can get a ton of flexibility out of your system in exchange for a little work filling out the fields.

Use area for product. Make your area tree structure mimic your application menu structure. This assumes that you have a seperate team project for each product or application you have.  We set our Area up to track project/subproject, but in retrospect I would have rather used area for product. We have a complex systems with many menus and the area tree structure would have handled that well. I would have made a separate field called Project and created a list of projects to drive that field off of.

Use iteration for time.  Track versions and iterations here. This makes it easy to plan which version and which iteration or timebox you're going to do work in. If you don't develop iteratively, no problem. Use only the top level of the tree structure for versions.

Create a field to capture project name. Call it "Project Name" or something that makes sense to your organization. Make it a dropdown list containing your projects and sub projects.
When you're done, you'll have something that looks like this:

• Team Project - System
• Area - Subsystem/menu/submenu
• Iteration - Version/iteration
• Project (you create this field) - project/subproject

With all this information captured in your work items, you can then get metrics out of the system regarding which parts of the system you did the most work in, which parts of the system had the most bugs and which parts of the system were the most costly to build. If projects don't match one to one with parts of the system, it's okay. You can get total hours spent for each project and see bug rates by project. You can track work done in the same part of the system using different funding sources.