Step 1: Gather Materials
Materials to be dyed. These should be primarily of silk or cotton, or an animal or plant based fibre. Not all of these dye equally, so be prepared to experiment.
Tea. It can be any kind, as long as it primarily contains tea leaves. If you have something old lying around, but hate drinking tea, now's your chance to get rid of it. Coffee will also work, and you can use coffee grounds that have already been brewed. It gives browner colours than tea. If you do use coffee grounds, makes sure to tie them up in a loose woven cotton like cheese cloth, or double layer of nylon tulle so you don't have to pick the grounds out of your dyed material.
Boiling hot water. Don't burn yourself.
A bowl or vessel to hold your materials being dyed and the tea/coffee grounds to dye them with. Make sure there's enough room for your materials to move around freely without the hot water spilling.
Step 2: Dying
Put the tea into the boiling water., and poke at it a bit, to get the dye to disperse. Add more tea, if necessary. When you think there's enough tea in the water, go find something to do for a while, while you wait for the material to dye. It can take anywhere from a few minutes for a light tint to an hour or more for darker colours. If you need a really dark colour, you'll get the best results from several dye sessions.
The cloth to the right of the bowl is what I was aiming to match the lace to during this project.