To clear things up: A Widget Area is a section of your website that can be customized by adding Widgets. It's usually the sidebar but they can also be in places like the footer depending on the theme. For example in the screen shot below I'm using the Twenty Ten theme and there are a crazy number of places that I can place Widgets! There are two sidebars and four spaces in the footer that I can place Widgets. Most themes will usually have just one or two Widget areas.

What we can see here are a number of areas in the Widget settings. The large section in the middle that says 'Available Widgets are all the types of Widgets that you can use in your Widget Areas. The narrower area to the right that says 'Primary Widget Area' is the main area, and this is usually the sidebar.

This is the bit where we get to play with our sidebar!

Since I'm a crazy minimalist (ha not really) I like to start with nothing in the sidebar and add exactly what I want… this is so I don't fall into the trap of thinking that I need a section when I really don't (meh, I'll leave it in there).

To remove a Widget, simply click and drag it out of the Widget Area. You can drag it anywhere you like and it will disappear.

Dragging a Widget out of the primary Widget Area.

Good, they're all gone.

Now we can start adding Widgets again to the sidebar. The first one I like is Search. The way to add a Widget is very simple - you guessed it, simply drag it into the sidebar. When you see the little dotted box appear the Widget will drop into place.

Drag the Widget you want from 'Available Widgets'...

… into the Widget Area.

When the Widget has just appeared you'll be required to give it a name, as well as changing any other options that the Widget has. Don't worry, you can change these later, and if you don't give it a name it will use the default for the Widget.

Now you can keep adding the Widgets that you want. Try and use as few as possible. The more content your website needs to serve, the slower it will get but more importantly the really important things that you want your visitors to see can get buried in a tidal wave of clutter. Keep it simple.

You can 'shrink' the Widget when you're done by clicking on the small triangle on the Widget. This is also how you expand Widgets in order to change their values.