Open your picture:
In the toolbar, click on the rectangle select tool.
Drag the rectangle over the picture in the spot you want, making sure to keep the dimensions exactly even:
For example, I dragged the corner carefully around until I got 190x190 in the bottom of the window. northern_star reminds me that you can also press and hold the SHIFT key after you start dragging, and the selection will stay completely square.
Go to Image--> Crop to Selection.
Your image should now look like this:
There is also a Crop Tool, which you might like to use better. saavikam77 says: I actually use the crop tool to crop. Just click and hold where you want the upper left corner to go, drag until you have a square selection, and let go. Click anywhere inside the selection, and voila! :) Cropped.
Resize the image by going to Image-->Scale Image:
In the dialogue box that pops up, change the width to 100, and make sure the link is still connected. Press Tab on your keyboard, and the height will automatically change to 100:
Your picture is now cropped and resized:
Now, that looks a bit oversharpened to me. Sometimes this happens when resizing a picture. I like to Filter-->Blur one time before resizing, and then Filter-->Enhance-->Sharpen after resizing. This gives me this look instead:
In the end, that's really up to you! Hope this helped. :)