Performance analysis and optimization – Which approach is the best?

For a number of years, I’ve had a successful online business, but as I’ve gotten more customer, and thus higher server load, the performance of the site has dropped significantly, which is obviously bad. Therefore I have investigated how to fix it, and have stumbled upon the expressions performance analysis and performance optimization, which both seem to be relevant in my case.

However, while there is a lot of information explaining the meaning of performance analysis and performance optimization, there is little information regarding the approaches one should take to apply these two concepts.

There are of course many companies who offer services involving performance analysis and performance optimization, but they don’t work for peanuts and besides, I’m kind of used to doing things on my own, in my own way.

Thus I ask you now, if you may be so kid as to guide me to at place on the net, recommend books or similar, that explains the steps I need to take regarding performance analysis and performance optimization. I may very well end up deciding that this task go beyond my abilities, but not before I have investigated the matter further, as I’m sure you can understand.