How long does the process of immigrating to Israel generally take for American Jews?

It's really up to you ,but generally it could take from 6 months to a year . Here are some useful info.in the second link it's the things you need to do before making an Aliyah .

I'm making aliyah in October. I began the process at the end of April. I could have left mid summer because I was approved. But i needed some more time. You get approved relatively quickly if you are makign aliyah but obviously people have personal things to take care of before they make such abig move. id give yourself at least 4 - 5months of preperations.

With bag packs etc etc. The legal procces takes around a 4 to 8 weeks i read somewhere i think.