You can select a portion of an image in Preview by simply dragging across the image with your mouse. You can copy and paste this selection, or use the Crop tool (Command-K) to get rid of everything outside the selection.

If you want to make a selection of a specific size, you normally just have to guess. By default Preview doesn't tell you the dimensions of the selection, but there is a way to make it.

If you hold down the Option key before making a selection on an image, a small grey box appears next to your cursor telling you the size of the selection in pixels.

This also works on already made selections. Hold down the Option key before dragging one of the dots around the edge of the selection box and the selection size will appear again.

When working with most image formats the select tool is the only one you have, so using it is simply a case of dragging across an image. If you are using a PDF file, make sure you are using the select tool by pressing Command-3 or by going to the Tools menu.