If you are smoking it, I would smoke about a cigarette worth at a time for noticeable effect. The old timers call it smoking a tasp. But honestly, smoking is absolute crap for your health.
Science actually weighs in on this one for me. Studies measured brainwaves of people exposed to various scents found in nature. When introduced to the smell of A. Vulgaris (mugwort) they found that certain regions of the brain experienced increased activity. So really, smoking it is not needed, IMO, as it is an olfactory trigger for your brain waves. In other words, it is the smell. You can add this effect by putting a healthy amount into incense or simply just taking a strong whiff off the top of a bottle of pure essential oil. When you burn it, it is the oils that contain the active ingredients. A difuser works too.
I use mugwort oil in this way before some meditation, divination practice, and when I have chest or nasal congestion (similar effects as Vicks Vapo-Rub).
Another thing; if you live in the States or in most of Europe then you are wasting money and opportunities to learn if you are paying for this stuff. It literally grows everywhere, even in the middle of large cities, but most mistake it for common ragweed. Look for it anywhere ragweed can grow. Like I said, it looks identical, except for two things: 1. Ragweed leaves will be a shade of green on both sides, but mugwort will be green on top and the underside will be almost whitish-grey. 2. Do a smell test by taking a sample leaf and crumpling it in your hand to smell the juice. If it smells like cut grass then it is ragweed. If it smells spicy, almost like a cooking herb, then it is mugwort. Once you get the smell test down you can easily harvest the stuff in total darkness.
It’s free, it’s fresh, you put your energy into the process, you learn a new thing, and there are more uses for the fresh herb than there are for the dried. So much winning.
This is important too. Don’t mess with the stuff if pregnant, and I would suggest not smoking it around pregnant women as well, for obvious reasons.