There's only really one method I know of that will likely cause you to get sick fast, and that's to spend time around people who have some form of infectious illness. That being said, even that's not a guaranteed method, and I'm not sure why anyone would want to increase their chances of becoming ill.
I've heard about plenty of things that will increase your chances of becoming ill over the years. To be honest, I learned about many of these things when I was a child, which leads me to believe that they're just ways of getting kids to behave in a certain way. Here's a couple of those myths:
Going outside with wet hair
This is a classic way to ensure that you're ill according to folklore, but in fact, it's all a load of nonsense. Illness usually manifests itself due to a virus, and having wet hair will not increase you chances of catching a bug. Unless you're outside in the cold for long periods of time with wet hair, you're unlikely to get hypothermia. Still, it's unlikely to feel good going out with wet hair.
Not zipping your coat up
As stated earlier, I reckon this one was simply used as a way to get kids to wear their coats properly. Still, I used to think that being cold was something that would increase my chances of getting sick. In reality, much like the wet hair example, having your coat undone isn't going to increase your chances of contracting a virus. It might be a bit cold, though!
Poor health
As a final thought, poor health is something that will increase your odds of becoming ill, but it's unlikely to be a quick process. A lack of sufficient vitamins and minerals will decrease your immune system's ability to ward off illness.