Logs are nothing more than a collection of status notes a system makes about a process. They are a way to review what happened during that process to understand what worked and what didn't. Most systems have some sort of logging option. Exchange has a couple of useful logging features that you've probably heard about - Message Tracking and SMTP logging.
Enabling Message Tracking is done in the Exchange System Manager (ESM). This is done at the server level. Open the properties of the server and find the checkbox on the General tab. That configuration also defines the location of the log files and the retention period.
Enabling SMTP logging is also done in the ESM. Although this is configured per server, the configuration is found in the properties of the Default SMTP Virtual Server (expand the server, Protocols, and SMTP).