The traditional way to finish a quilt uses bias binding sewn to the front, folded around to the back, and whipstitched by hand all around the back. This is a real pain in the rear for quilters like me who are used to doing everything on the machine. I don't hand sew unless my very life hangs in the balance.
But you can bind a quilt by machine if you flip things around and do it all backwards. This tutorial will show you how to use traditional bias binding and attach it to your quilt by machine. You need a quilt top, batting, backing, and bias binding for this tutorial.
Step 1: Make your sandwich
Layer your quilt together and baste. How you do this is up to you. There are eleventy billion ways to baste a quilt and I'm not about to tell you what way is better. It's really a matter of personal preference. I use basting spray because it's fast and easy and there is nothing to remove from the quilt when I'm done. I dig that.
Step 2: The dreaded "quilt as desired" and then trim
Do your quilting and then trim the backing and batting evenly with the edges of your quilt. (I know the red thread is totally fug but you can see it really well in pictures so there you go.)
Step 3: Make/Acquire/Conjure Bias Strip
You need enough bias strip to go all the way around your quilt plus about ten inches for corners and overlap. Fold your bias strip in half and press the whole length. The bias tape you buy in little packets isn't going to work for this unless you unfold it and press it because what you want is a double layer of bias tape with both raw edges matched up on one sides. Take the strip, fold it in half, and press. It's really not complicated so don't think too hard about it, just do it. Fold, press. That's it.