Simple: learn to knit, crochet and sew
The best way to learn to knit or crochet is to find a willing tutor. Failing that, youtube has some wonderful tutorials to get you started (here's my knitting and crochet posts). Start with something simple so you don't feel like giving up when it doesn't work out. Knitting and crochet are the cheapest options, as you will need a sewing machine to get started on sewing, but look for secondhand, lots of people have them and never use them. Try not to stockpile lots of supplies of wool and material, or you still spend more that you save, but I know that's not easy! And try to make things that you would have otherwise bought.
Simpler: make soap and other personal needs
Soap is easier than it sounds, and if you use tallow it can be relatively cheap. Soap can be used instead of shampoo and body wash, and can also be used for washing dishes. You can also make deodorant and simple salves. Reusable menstrual products are a huge saving (here's the whole story for those who want to find out more).
Homemade soap (details here and here)
Homemade deodorant (recipe here)
Homemade skin salve (recipe here)
Simplest: preserve, dry or freeze some excess produce from garden or bought in bulk
I use my dehydrator all the time, its great for keeping the excess herbs (including chilli flakes and garlic granules), but I've also been air drying them recently now that the weather is less humid. I also freeze lots of beans and cherry tomatoes from the garden, and other produce that I've can buy cheaply in bulk. If you're lucky enough to have a pressure canner, that is also a great way to preserve any excess vegetables and fruit as well, although you can use a waterbath method for high acid produce.
What do you think? What are some other skill that help to get started with a simple life?