Being an assistant is a job, not school. If you learn anything about photography it is by setting things up and watching. But there isn't much time to watch. A shoot is usually a very busy place. If you're lucky, as I was, and work with friendly photographers you can also learn during travel times by chatting. Just don't make a pest of yourself.
You may need a portfolio but since you would not work as a photographer this portfolio has a very different role. You want it to show a basic understanding of photography, yes, but mostly an understanding of your job. Shots with studio lights, shots of models, etc. You're trying to show your understanding of equipment and attention to details more than anything else. But to be honest most photographers I interviewed with barely glanced at mine and it was only 8 photos.
I have been told here that since the advent of digital photography, there are fewer jobs for assistants. Although it is quite true that I spend quite a bit of time loading and unloading film from cameras it was not the biggest part of my work. And I never dealt with the films after the shoots. My photogs used couriers to get the stuff back and forth to the labs.
Back when I did it professional associations kept a directory of available assistants. I imagine they still do. Try and look at them to see what those people are saying about themselves. That will give you a very good idea on what to do then join the association that fits best what type of photography you want to work in and get your name in there. It should also give you a directory of members which will allow you to check them out (their websites) so you can go knock on doors.
Be aware though that it is rarely a full time job when you start and, with some photogs, it never will be. Not every photog needs a full time person. So you need to know how to sell yourself on a near constant basis unless you get lucky. Which could happen.
As with everything else, social contacts are very important. I got my first long lasting job from a a guy I knew. I had bought equipment from him and we hung out in the same camera store. Since he didn't need me full time, he then talked to a friend of his. Those are the two guys I spend around two years with. After a while, they liked me so much that they talked to each other when scheduling their shoots.
So, think of who you know who knows someone who knows somebody.
Good luck.