When I first started quilting, I really struggled to understand cutting fabric. It seemed like something that should be easy but it really is an art form to cut fabric efficiently and with as minimal waste as possible. If you're just starting out with quilting or just want a new perspective on fabric cutting, read on!
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understanding fabric yardage
Before we start cutting into the fabric, you'll want to understand how the fabric is set up. When you purchase any quilting cotton yardage from a fabric store, it'll be cut directly from the bolt depending on the amount of yards you require. The fabric will have a fold along the top and a selvage edge along the bottom.
The fabric length is determined by the amount that you order. When you order 1 yard of fabric, your length of fabric will be 36 inches from the left side of the selvage end to the right. Most fabric providers allow you to order in either 1/2 or 1/4 yard increments.
The fabric width is how wide the fabric is when it's unfolded, from selvage to selvage. For most quilting cotton, this will be 44 inches. Since you'll be removing the selvage edges when cutting the fabric, I recommend to use 42 inches when calculating your fabric requirements for your quilt.
how to cut quilting fabric
Make sure the fabric is folded so that the selvage ends are all aligned on one side. Fold the fabric into as many layers as you feel comfortable with to have a shorter cut length. Trim the selvage off using a ruler and a rotary cutter.
Unfold the fabric back to how you started, with the original fold along the top and the trimmed selvage edge along the bottom. Fold the fabric horizontally into as many layers as you feel comfortable with, making sure the top fold meets the selvage end. Trim the right side of your fabric using a rotary cutter and ruler, making sure all of the edges are square with the ruler.
Rotate the fabric so the end you just trimmed aligns with the required measurement on your ruler. If you need 4-inch squares, your fabric should align with the 4-inch marker on your ruler. Using your rotary cutter, trim along the ruler edge so you cut a 4-inch strip. Set this aside for now and continue cutting to the amount of strips you need for your quilt. 
Set out your strips by staggering or stacking them to your preference. Make sure the folded edge is on the right side and do not cut into this fold. Align your ruler on the left side of the strips and if desired, trim a small amount to align the strip ends perfectly. Cut the strips into squares using the same measurement as your strips (for example, 4-inches for 4-inch squares).
Continue this process until you have cut as many squares out of your strips as you can. Depending on the size of your squares, you may be able to unfold the pieces along the right side to cut more squares. If not, these pieces can be scrap or used for another project. 
Continue this process for the different fabrics needed for your quilt, & pat yourself on the back!