The simplest and easy to understand definition is from Wikipedia - Project management is the discipline of planning, organizing, and managing resources to bring about the successful completion of specific project goals and objectives.
The time tested method for implementing Projects has 5 Stages.
Namely,
- Initiating the project
- Planning the project
- Executing the project
- Monitoring and controlling the project
- Closing the project.
- Wild Enthusiasm
- Total Confusion
- Disillusionment
- Search for the Guilty
- Punishment of the Innocent
- Promotion of the Non-participants
Here are few links for further study.
http://www.ittoolkit.com/qtools.htm
http://www.method123.com/project-management-tool.php
Here is a simple presentation explaining the project methodology
Project Management Basics