Step 1: As with any design tutorial, you'll have a specific program opened and being used to generate the end results. What you need to do is capture your current actions in an image so that you can then place them on a tutorial page. Say, for example, that I'm doing a tutorial using Photoshop. I would have Photoshop open and prepare the first step of whatever design I'm working on. When I have my first step prepared, I hit Alt + Print Screen on my keyboard. This copies your screen to memory/clipboard.
I use Photoshop to crop my screenshots. So whilst still in Photoshop, press CTRL + N on the keyboard to open a new document. Because you have your screenshot saved in memory, Photoshop will autmatically fill in the height/width details to reflect the size of the screenshot in your clipboard. Click Ok, and then hit CTRL + V to paste in your screenshot:

Step 2: As you can see, the entire screen was captured. We don't need all of that, so crop out the part that you want by using the Crop Tool to highlight the area that you want to save.
Step 3: Once your selection is complete, double-click on the highlighted area - this should leave you with everything inside the area you just selected:

Step 4: We could keep the image like this, but I don't like the gray area that's still left, so let's get rid of that. To do this, use the Magic Wand Tool to click anywhere inside the gray area - this will form a selection of the entire grey area:

Step 5: Now right click on the gray area and choose Select Inverse. This will select just the screenshot alone:

Step 6: Go to Image > Crop and you'll have yourself a nice screenshot to use on your tutorial page!

You may notice the top corners still have some gray showing. You can use the Magic Wand Tool to select the gray and then hit DELETE to get rid of the gray if it bothers you!
Alternative Method
Another technique for creating screenshots involves changing our proceses above at step 4. After using the Magic Wand Tool to select the gray area, hit DELETE on the keyboard to get the following:

You can now trim off the transparent pixels by selecting Image > Trim from the main menu with the following options:

And there you go, two great ways to create nice screenshots for tutorials! Enjoy!