if you bought an aftermarket intake, the stock intake won't have any parts remaining in the engine bay and you won't hook anything up to it. It should consist of some tubes and couplers and an air filter. all of which get assembled into a pretty little tube. you attatch the one end to the throttle body, and the other end gets the filter. it's a pretty straight foreward job. as long as the intake was actually made for your car, it should fit in no problem. Since the person knew it was on "wrong" perhaps they could show you how to do it correctly. I doubt you have it on wrong. it's too simple to mess up.
as far as the lag, give a better description of the problem in some detail and I"m sure we'll be able to diagnose it.