There are many resources for finding out where others are advertising. As for the most cost-effective tool, that's dependent upon what you offer and your target audience. If it's for products, consider Google Shopping.
Note that any advertising is an investment. If you have zero budget, consider other ways to build capital first so you can re-invest it. You'll find that you need to spend a decent amount on advertising first just to gauge exactly how you should be presenting content and bidding.