There are 2 different types of crops that can be done in Photoshop. The first uses the crop tool. Selecting a 1:1 ratio will allow a square crop to be made. After the crop has been made, the image can be resized.
If you want to take a fixed pixel sized crop (such as 750x750 pixels), the marquee tool needs to be used. By setting the marquee tool to a fixed size, it is possible to make an exact sized crop.