I am experimenting with different styles in Photoshop & Illustrator. I am trying to make different shapes and styles in Illustrator 10, and color it in in Photoshop CS2. I want to use vibrant colors like in this piece of work:

http://nkeo.deviantart.com/art/f3fb3f-and-f9326b-64632083

Can somebody lend a hand?

It's all about color choice; experiment with different vibrant colors. Part of the "vibrance" is the blending mode that the designer used. It's the "outer glow" effect. Right-click on your layer in Photoshop, and then go to "Blending Styles." From there, look on the left menu and you will see, "Outer Glow." Adjust the settings to your liking.