Cognos is a business intelligence reporting tool. It is meant to query over data sources including data warehouses and data marts, to help provide insight into your data and help you make decisions, view trends, etc. Here is IBM's Cognos product page. Here is a definition of Cognos from Wikipedia which I find helpful.
Drools is a Rete algorithm based Java rules engine that allows you to define business rules within your application and then have your application validate against those rules. Here is its definition from Wikipedia. And here is the Drools community page.
We actually use Drools in some of our applications for client side verification of business rules. And our business is planning on using Cognos (and another tool called QlikView) to do business intelligence reporting over our data warehouses and data marts.
As for how you use Drools, I'd look at the community page. In the version we used (2.0-Beta-10, which was way before Drools was acquired by JBoss) you generally define your rules in XML based files with a .drl extension from what I remember. We use an older version of Drools so it may have changed since then. We also extended Drools in our case so we could write our rules in Java code for run time debugging versus using XML files (since our Business analysts weren't writing the rules anyway).
Hope this helps!