After seeing this demo: [Mini-Tutorial] Blend 3: Rich Interactivity with No Code and the cool way she was able to simply drop a "Behavior" on a button and a menu displays (and allows you to set some properties using simple drop downs no less) and then the button is now able to make another element move, I had to learn how to make behaviors.
There are examples on the web but all the ones I found were based on the Silverlight 3 preview and with the released version of Silverlight 3, there have been changes.
I decided that for my first behavior I would start with something extremely simple. I wanted to make a behavior that you could drop on one element, and when that element triggered the behavior, the text in a TextBox would change to lowercase.
This assumes you have Visual Studio installed. Also install:
Open Visual Studio and select File then New Project.

Select the Silverlight Application template.

Use the option to create a website to host the project.

Visual Studio will create a Solution. Right-click on the solution in the Solution Explorer and select Add then New Project...

This time create a Silverlight Class Library.

In the Silverlight Class Library, add a reference to the System.Windows.Interactivity.dll assembly located at:
C:\Program Files\Microsoft SDKs\Expression\Blend 3\Interactivity\Libraries\Silverlight\System.Windows.Interactivity.dll
Rename the Class1.cs file that is automatically created to "MakeLowercase.cs".
Replace all the code in the MakeLowercase.cs file with:

Build the project.

In the main Silverlight Project (not the Silverlight Class Library that you just created the behavior in), add a reference to the Silverlight Class Library that you just created the behavior in.
Build the entire Solution.

Right-click on MainPage.xaml and select Open in Expression Blend...

In Expression Blend, add a Button and a TextBox to the design surface of MainPage.xaml.

Click the Assets button.

Select the Behaviors group and you will see the MakeLowercase behavior.
Drag and drop the MakeLowercase behavior onto the Button.

In the Objects and Timeline window, the MakeLowercase behavior will be attached to the Button.

When you click on the MakeLowercase behavior in the Objects and Timeline window and look at the Properties window, you will see that the EventName in the Trigger section is set to Click. This means the behavior will fire when the Button is Clicked.
In the Common Properties section, the TargetName is set to the default value of [Parent]. This wont work because the target must be a TextBox. You can click the round "bullseye" symbol next to [Parent] to enable the Artboard element picker.

You can then click on the TextBox and a popup will display indicating the TextBox will be given a name. Expression Blend is smart enough to know that the code wont work unless the TextBox has a name so it does it for you.

In the Common Properties section, the TargetName is now set correctly.
Save the page.

Switch back to Visual Studio and right-click on the .html test page in the web project and select Set As Start Page. Also right-click on the web project and select Set as StartUp Project.
Hit F5 to build and run the project.

You can type in the TextBox

When you click the Button, the text will change to lowercase.
You can see the live example at this link.
You can download the source code at this link.
My CodeProject Blogs