There are several things to check. First, how are you starting the Quartz Scheduler? The Scheduler acts like a service and needs to be started in order to load and schedule Jobs.
The best advice that I can give is to point you to the draft chapters of the book that I'm writing on Quartz. You can find the draft chapters on the main Quartz site: http://www.opensymphony.com/quartz/book_chaps.html.
Chapter 13 covers using Quartz inside a web application. Quartz can be started and ran from a web application fine, but there are some steps that must be taken because it is a web app and runs within a web container. For you first Quartz app, you might consider running it as a stand alone J2SE application. It will be easier to understand. There are several chapters out there that will help you better understand the framework.