How do I draw a rectangle of a specific size? I need to draw one that is 1072 pixels wide and 620 pixels tall.
In Photoshop CS6, simply click on the canvas with the Rectangle tool selected, them enter the width and height.
In versions prior to Photoshop CS6, you can set the size in the shape options, before to drawing the shape itself (please see the other answer on this page for screenshots and more info). This also works in Photoshop CS6, but a single click on the canvas is easier, if you have CS6.
You can also draw the shape while watching the info panel, and/or adjust afterwards by nudging (make sure you have pixel snapping turned on, so you're adjusting in whole pixel increments).