Simple stuff starts with CPU, RAM, disk IO of your webserver, usually via SNMP or WMI, using something like SCOM or Nagios or MRTG. if your CPU is pegged or you've used all your RAM, you've probably got a problem. There's a lot more you can monitor on the server, but those are the basics.
More advanced performance monitoring is using an external host with a browser agent to run certain browsing or transaction operations against the website, and measure the response times; if it starts regularly peaking above a desired response time, it's time to upgrade something. What it is that needs to be upgraded can sometimes be determined by the above simple monitoring, or it may require a deeper dive into your web application's code.