WHAT YOU'LL NEED
A DARNING EGG
The purpose of this tool is to rest against the wrong side of your fabric and provide you with a firm surface while you work on the right side, mending the hole.
If you don't have a darning egg, that's okay. One can easily be improvised. Ceramic or plastic eggs can be used as well as old door knobs and even light bulbs. For small holes, you may find you are able to do without and just use your hand.
THREAD TO MATCH YOUR FABRIC
This is important as you don't want to create a lumpy mend, by using a thread that is too bulky or too thin, especially if you are repairing socks or an undergarment. I find that cotton sewing thread works well for socks. Heavier gauge quilting thread works well for canvass or heavy jean materials. Yarn is used for crocheted or knitted work.
A NEEDLE TO MATCH YOUR THREAD
If your needle is too small, you will find it difficult to get your thread into the eye. If your needle is too large, you may find yourself fighting to force it through the fabric, especially when the bulk of the needle's eye passes through.
A RUBBER BAND OR TWINE
This is to secure your fabric taught over your darning egg. You don't want to place this too securely, and you CAN do without it. I find that with small holes, it is nice to have the egg stable, not sliding around behind the work. A rubber band helps secure your work to your egg. If your hole is very large, you may not want to use a rubber band, as it may push your egg through the cloth.
SOMETHING WITH A HOLE IN IT
A sock is a good starting project. It's very forgiving. If you are not well pleased with your results, no one will see your first attempt. If you must throw it out and start over, it's no real loss. Additionally, these usually present the beginner with small holes to gain experience before someone accidentally manages to rip your upholstery. Consider using a sock that has a contrasting color to your darning egg. It will make it easier to see your thread.
To begin your project, choose a well lit area where you are comfortable. I find that when I'm learning a new skill, it is helpful to select a less hectic time of day when I have fewer interruptions. (That almost made me laugh when I typed it.) If you are a mom, this is a relative thing. Just assemble your materials near your favorite chair and steal a moment when you are able.
STEP 1 -- WARP YOUR LOOM
Do what to who? I know we aren't learning how to weave on a loom here, but the principle is the same. Just as you would place your warp thread on a loom using a figure eight pattern, you will do this with your darning. The fabric is your loom and your thread, at this stage, is your warp yarn.
Use your needle to go under the edge of the fabric and come back out the right side. Then go back down into the hole of the garment with your needle, under the opposite edge and repeat. This creates a figure 8 looping as you see in the illustration. Be careful to work far enough beyond the edge of the hole so that you are anchoring your warp into secure stitches.
Take care not to pull the thread too taught as you will want to keep the same tension as the garment and surrounding fabric. This will keep it from puckering when you begin to weave in your weft thread.
STEP 2 -- WEAVE IN YOUR WEFT
I know, again you're thinking I've left the topic. No, the weft yarn is your same thread now working in a horizontal over and under pattern. Use the point of your needle to weave over and under the warp threads. You can also use your needle to push the weft thread snug against the warp as it is threaded back and forth. At the end of each row with your weft, use your needle to place an anchoring stitch into the garment.
Continue alternating your weft over and under the warp threads in alternating patterns until the hole is mended.
Here's a video of a woman darning a knitted sock. She uses a darning mushroom. It has a larger and flatter surface, very similar to a doorknob.
How to darn a sock