NNNNNNNnnnnnnnnnnnaaaaaaaahhhhhh!!!! Other guy making things to be super complex! first than any thing else, LED's are designed from the ground up to use only 3V, You can use 12 ! but you will be having to buy at least one 100 oHm resistor! to bring down the resistance at the level of the LED!
U can buy LED's that are rigged from the factory to use 12V, but you will pay ten times as much just because they solder the resistor for you. The bridge rectifier is a good Idea! but expensive, you can use a single Diode, on one of the leads! that will give you a clean polarity! No need for capacitors or any thing else!
Now if you don't have any of this electronic components! and you are going to buy them any way ! just buy one transformer one diode and one potentiometer of 100 ohm and as many LED's as you may want! all of this is available on Radio Shack! and make sure you buy a really small transformer! about the size of a tangerine, ask the people on radio shack to connect the power cord for you! in that way you will be safe from electrocution.
Good luck and have fun!