Step 1: Things you will need
-fabric, however much you want depending on the size of your blanket. I like to use polar fleece types of fabrics, but I have also used flannel for thinner blankets.
-Blanket binding, enough to go around the entire edge of the blanket. You should be able to find blanket binding at fabric stores, but if you can't find any, you can use satin ribbon, at least 2 inches wide. Iron the ribbon so it has a crease down the center and it becomes blanket binding!
-sewing machine (I guess you could do it without a machine, but it would take ages)
-pins, lots and lots of pins
Step 2: Prepare your fabric
Sometimes when you buy fabric, it can be cut at an angle or it gets stretched out and will not be in a perfect parallelogram. If that's what you're going for, then go ahead to the next step, but if you want a square or rectangular blanket, take the time to make sure all the sides line up evenly. Do this after you wash (and iron) your fabric. Give the cut off pieces of fabric to your cat.
Step 3: Pin on the blanket binding
To wrap around the corners, pin the binding close to the corner, then pin it on the other side of the corner, as you have been pinning the binding to the blanket. You will have some parts of the binding sticking up, so fold it down on either side of the fabric and pin it down for a nice, neat corner.
Step 4: Sew
To turn a corner, sew 3/8 inch to 1/2 inch past the next side, make sure the needle is down and all the way through the fabric, raise the presser foot and pivot the fabric around the needle until it is facing in the direction you now want to sew and then continue.
Step 5: Finish!
And then you're done! Enjoy your snuggly new blanket, or give it as a gift!