I'm speaking of RC paper, but I would go against many of the recomendations to wait until the tea has cooled down. In my experience I did not achieve an acceptable result from cool tea. The best results I've had were using a pre-soaked RC print soaked in very warm water then the water is removed from the tray along with the print. The tea is poured into the tray, while not boiling I've had best results with it still very hot. Let print sit in the tray and agitate randomly for a period of 5-10 minutes, beware, the prints tone will darken as it dries...much more than you'd probably think.
I've never done this with fiber.
For a darker look try about 3 scoops (tablespoons) of ground coffee with about 12ounces of water for 1 8x10print, again, in my usage it only seemed to work how I expected with hot water.
Good luck!
(I've had prints that were stained a year ago in only tea, only coffee and a combination of coffee and tea and none have shown any ill effect)
Sidenote:
I stained a print blood red with Kool-AID over a year ago, where it was very difficult to get correct and too much washing will remove the tone completely it definately works for creating 'wild' color youd normally not see. Try 2 packets of powder and about 6ounces of water (the less water the easier it stains, on RC glossy during the wash you can remove as much or as little of the stain as you want) for 1 8x10 let soak for 20 or so minutes with random agitation and wash until you get the tone you desire... it wont be sticky and touching the surface will leave fingerprints, it definately seems to 'keep' after staining as the print I created over a year ago still looks very red and doesnt seem to be eaten away or attract ants or anything of ill effect, seems crazy, I know...... but it really does work! (o yes, watch those hands unless you want red or blue stains on them you should wear gloves!)