Just some quick and dirty answers...
First of all, don't worry about pitcher development so much as getting your conditions correct. Some things to note...
--It is probably an N. x Ventrata if you picked it up at a Garden Center, but seeing as I don't have Alata or Ventrata, don't quote me on that.
--Make sure you are using distilled or rain water. Looking at your water dish, it looks like you might be using water with some dissolved minerals in it. This is fairly important.
--What direction is the window it is growing in facing? Try anything but a North facing window for starters, but I would pick your sunniest window.
--This plant is very easy to take care of, especially on a windowsill. Don't worry about the humidity/spraying of it constantly. After a month or so it will acclimatize.
Once you get decent conditions, and the plant has 1 month+ to settle in, you should see some pitcher development. You have stumbled upon a wealth of information, feel free to ask questions, and welcome!
p.s. You can cut the dead pitchers off at the tip of the leaf if you wish.