To answer your first question: this information is very well documentated in the Autophagy Handbook available at Novus Biological. I picked up this handbook on a congress last year and actually used it a lot this week. there you will find modulators and how to study. You will find it here:
The effects can be positive or negative. Here are some review articles that address autophagy and cancer. Article Principles and Current Strategies for Targeting Autophagy fo...
The easiest way to induce autophagy in cultivated cells is via nutrient deprivation, induced by simple serum starvation of your culture. Alternatively, chemical induction can be achieved with rapamycin or simvastatin, among others.
However, there is no simple answer to the second part of your question. Autophagy might be a pro-survival mechanism, occurs in parallel to apoptosis or even leads to autophagy-associated apoptosis, a rather pro-death effect of autophagy. For the evaluation of autophagy, I recommend to analyze apoptotis induction as well. Also, you could look at the crosstalk of apoptosis and autophagy by evaluating Bcl-2 and beclin-1. I highly recommend to read Daniel Klionsky's (community-approved) guidelines for monitoring autophagy prior to performing any experiments in the highly complex field of autophagy evaluation (doi: 10.1080/15548627.2015.1100356). You should find answers to many questions in this publication, which will also be updated in the near future.