You did the proper method for quickly acclimating the yeast to a no oxygen environment. When using dry yeast, you want to mix in some warm water (~100F) and get all the lumps out. Then add a pinch or 2 of sugar, and then really mix to froth it up (getting lots of oxygen into the water). Then let the mixture sit for 10min or so and add to your bottle (that has dissolved sugar water at about the same temp). This should create pressurized CO2 within the hour, and by 2-3hours (depending on water hardness/etc can vary) should be producing at full rate.
While malkore suggested not to shake once mixed, personally I gently shake (in a circular fashion) to resuspend any yeast sitting on the bottom, as well as to evenly distribute the alcohol that is produced, and the suger in the water. As long as you don't overdo it (and don't have the bottle too full in the first place) I've found this to produce a more even CO2 production as well as slightly decrease the longevity of the mixture (I'm guessing this is due to the more even CO2 production whereas if you didn't shake it the CO2 production would slow near the end prior to alcohol poisoning).
You should get a minimum of 10-14 days out of the mixture, but I normally change the bottle once I get close to 1 bubble every 1.5-2 seconds (optimal for me is around 2 bubbles per second), which for me recently has been about 15 days (I think, I tend to forget when I make the mixture as it doesn't matter as long as I don't let the CO2 drop to much, thus causing algae problems).
HTH,
justin