1. Weight out materials and grind them all to a powder.
2. Put the plant matter into your non-aluminum pot.
3. Add bottled (drinking) water, enough to cover the material by almost an inch.
4. Add .5-1oz (15-30ml) lime (or lemon) juice.
5. Turn on the stove, bringing the water to just below a simmer. Either heat the water until little bubbles start coming up and then back off a tad, or slowly increase heat until you see steam coming off the top and the surface of the water begins to "shimmer" or "gleam" a little.
6. Allow to cook for 30-45 minutes. Watch that the brew does not boil, stir occasionally.
7. Turn off heat, let the brew settle for a few minutes so that it can cool. Strain into a separate larger container through an old t-shirt, handkerchief, rag, or cheese cloth.
8. Keeping your colored brew separate, repeat steps 2-7 at least once or twice.
9. Put your plant matter aside (don't throw away until the day after) and combine all of your colored brew in your brewing pot.
10. Bring to a simmer, at most a low boil, to reduce the amount of liquid to something you consider drinkable. 8-16oz works for some.
Notes:
1. fine powder, more surface area on particles increases extraction efficiency.
2. lots of people don't like cooking with aluminum for any type of consumable, Alzheimer's or something.
3. bottled water works better than tap water, depending on the location. this may not be the case for some, but if you don't know then use bottled water.
4. this step is not totally necessary (pure water would work), but citric acid lowers the pH and increases the ability to extract alkaloids. it sits sour in your stomach and affects the flavor of your purge. some people use vinegar and boil it off, but I've found that vinegar is still gross. there's probably a correct amount of citric acid to use in accordance with your water, some proper ratio and if you have litmus paper and really want to be spot on, aim for pH 4. otherwise a littl' dabl' doya.
5. boiling hard breaks up the good stuff and thus decreases potency.
6. brew all day if you feel like it. some people like to. others say 20 minutes per brew/strain. 30-45 will get the job done.
7. handkerchief (cotton) works well if you've got a fine powder.
8. brew/strain at least twice, anything beyond four times is most likely negligible.
9. sometimes you may want to save your plant matter to throw in with the next batch, for fun. maybe you think you can squeeze more out of it. you won't know until after the session.
10. at this stage, the alkaloids are in their citrate form and will not be destroyed by a little boiling, so it is safe to use more heat.
There's a lot of other ways to brew, and it can get interesting to read around on the different methods. Someone who is interested might want to find different forms of preparation, try them separately, combine some ideas, until a personal method is developed.
I read about this girl who started off by adding the powdered plant material to the pot of a Mr Coffee with a bottle of water and some lemon juice. She just turned it on and let it sit for an hour (since it doesn't boil) and then strained it through a wash cloth into the ceremonial coffee mug. Kinda messy, but about as simple as you can get. Brews probably wouldn't be as strong as the above method, but it could work.
Keep in mind that sometimes aya (or mimosahuasca) just doesn't work. Try to not purge for an hour if you can. If effects are considerably less than expected, and you're working with ingredients of known potency using proper preparation, eat half a piece of bread with a lot of butter or just a few bites of something greasy. This can kick start a supposedly bunk brew.
It doesn't hurt to brew up 1.5x-2x what you expect to drink so that if things aren't as strong, you have the option of consuming more after a few hours.