i infuse the tea until i dont like its taste anymore/ or until taste
fades beyond my ability to enjoy it.
most of the time 3-4 infusions

the teas i have i already know about how much tea, water and how many
times i can re-infuse. for new teas one has to experiment.

What tools to use? whatever i put my hands on:
any sort of cup/mug, (usually 10oz cup, or a little 4oz gaiwan)
throw leaf in it,
pour water,
let infuse,
strain into different cup / or if already used the egg-mesh infuser no
need to strain

How long between infusions?
depends on the tea, and derived from experimenting:
green, oolong, black(china) i wait less than 10 minutes,
for black the most i done is 1 day. :P
(remember, the wet leaf kind of continues brewing after taken out of
the water).

after 1-2 infusions i adjust time(increase) or water(decrease)

(i usually also let the wet leaf wait around for 1-2 days - to see if
it grows anything
,in 3 years only 1 time it grew fungus - so i suspect it was probably
not from the tea.)