How do you caffeinate water?  Is there a formula available on the web?

Well; try mixing caffeine and water... Calculate how much caffeine to
add per gallon/liter and dissolve in water by stirring or shaking.

I wouldn't take advice in mixing chemical compounds from someone named 'arsenic.'

Just kidding. =)

Don't feel bad for the joke respree, I wanted to make one too...

Apparently commercial caffeinated water uses caffeine that originated
in coffee:

"Solvent decaffeination is a chemical process in which beans are
softened by steam and water, flushed with a solvent, usually
containing chlorine, and caffeine combines with the chlorine, then the
solvent is drained and the beans are heated with dry air to remove the
solvent. This process is repeated about twenty times to generate 97%
caffeine-free coffee.

Caffeine in colas is originally from coffee--The caffeine is removed
from coffee and resold commercially for use in Pepsi and Coke, and
Water Joe, a caffeinated water now on the market.

Water decaffeination--A newer method, in which green beans are soaked
in near-boiling water for several hours, and the water is then
removed, containing the caffeine."

http://essenes.crosswinds.net/xcoffee.html

Caffeine has a naturally bitter taste. Some of the commercial
caffeinated water products claim to have no taste, but how they
achieve this is a closely guarded secret.

Crush an OTC stimulant (e.g. NO DOZ), add to warm water, and shake
well.  One tablet = 100 mg caffeine, about 2/3 rds a cup of coffee, or
about two colas....or just drink any diet cola (about 50 mg caffeine).