The very best book on the market is Izzy Pludwinski’s Mastering Hebrew Calligraphy. You cannot do better than start with this.
Lessons over the internet
Learning with me over the internet.
Mezuzah study guide
A textbook for learning mezuzah-writing is available here.
Standing-on-one-leg summary
See also the halakha sections of this site.
A sofer works on parchment with kosher ink. You can use these materials to learn on, but they are immensely expensive, so you are better off starting out with ordinary calligraphy ink on ordinary printer paper.
When you are ready, move to learning the letters for safrut. Learn the letters and the halakhot of how to make them simultaneously, otherwise you will form bad habits. Here is a worksheet, and you can find videos on youtube. From this point, having an expert look over your work now and again will help you, but it is still mostly about practice.
Learning to cut a quill: here is a video (free), and youtube is full of others. Here are several websites. You can buy materials here. Now practice a lot. Use Google to learn some basic knife techniques, they will make your life easier.
Lefties: you have it harder learning English calligraphy, but you will have a fantastic time once you start doing Hebrew.
Timescale
How long it takes depends on you. If you are a good calligrapher and fluent in rabbinic Hebrew, you can become minimally competent in weeks or months. If you are starting from the beginning in both, you can become competent in a year if you put enough time and effort into it. It will take longer if you put less time into it.