Rather it's for business or personal learning. One of the basic tool that you should learn to master would be Discover the Lasso for Making a Selection & Edit:
This is one of the most basic steps you can learn in Photoshop for the purpose of creating graphic design. You must understand these fundamentals if you want to be a serious graphic designer.

Learn how to use the different options of the magic wand and other different tools to do some advanced selection modification to end up with your final result (such as a person separated from a background). Magic Wand for Making Selections & Selection Mod
 

Learn how to use the    Clone Stamp tool 

Learn how to use the    Crop tool

Learn how to use the    Elliptical Marquee tool

Learn how to use the  Eraser tool

Learn how to easily create and manage basic vector shapes as shape layers or fill pixels. Discover & Manage Basic Shapes

If you goal is to just create that Perfect Logo in a short period of time then you may want to look at learning how to create a professional looking logo in minutes. Logo in minutes or learn to create a professional web logo for your company or business, or just for fun using this tutorial. Professional Web Logo. Learn to create a trendy logo for your interfaces or art using this tutorial. Basic Logo

And for the most advance learn the steps used to create a fully detailed free form interface from start to finish. Freeform Interface Walkthrough

If you lost a button lately and you have been searching everywhere for that vintage or Antique button well forget about it and learn how to create your own. We will show you  in this Tutorial how to create an old looking button for your site. Lost no more! Old Button
And if that's not what you are looking for how about your very own 88x31 ad button. 88x31 Button Logo

For those that just want to get right to it. We will walk you through some processes used to create some realistic icons. For this particular Tutorial we will be creating a realistic pen that is sure to spice up your desktop or your next project. Realistic Icons with Photoshop

In Photoshop 7 the Pen Tool is the toughest tool for beginners to master. Here are illustrations, explanations, and exercises to help you get started. Basic Pen
 

The Clone Tool is a very valuable friend that makes quick work of removing these spots. Clone Tool The Clone Tool copies or clones a few neighboring pixels from one area to another.

Use the Magic Wand Tool  for Layer Masking: Night & Day  fills and gradients to create some night and day-fade effects.