What are the ways to find bottlenecks in a web application?
Regarding bottlenecks on the application server, you can use a profiling tool to see how much time is spent in each part of your code, how much memory is used, etc. For PHP, webgrind seems to be a popular, GUI-based way of profiling. Something like dotTrace would do the same thing for an ASP.NET app. Note that when it comes to databases, profiling tools like this will only show you which database queries are slow--not why they are slow. For that, you'd need to look into database-specific profiling...
Another aspect of web app bottlenecks is how much time it actually takes a browser to downlad everything (CSS and JavaScript imports, images, etc.) and render the page. There are several companies like Keynote who have bots that will hit your site from all around the world, analyze the performance, and give you recommendations about changes you can make to get the output of your app to the browser and rendered as quickly as possible (e.g., "use gzip compression and put your JavaScript at the end of the page instead of the head", etc.). You can also do this yourslelf on a much smaller scale, of course. For example, Firefox plug-ins like Jiffy and YSlow will do the job.
For any web app, you can try using the Firebug extension, along with the Yahoo YSlow extension (to Firebug). Really helpful in page performance.http://developer.yahoo.com/yslow/