how does one identify why a website is slow?

This is a great tool to find the speed of web pages and tells you what makes it slow: https://developers.google.com/speed/pagespeed/insights

I think one of the important thing that is missing from above answers is the server location, which can play a vital in web performance.

When someone is saying that it is taking a longer time to open a web page that means high latency. High latency can be caused due to server location. Let's assume as you are the owner of the web page then the server and client are co-located, so it will have a low latency.

But, now if client is across the border, then latency time will increase drastically. And hence a slow perfomance.

Another factor is caching which drastically affects the latency time.

Taking the example of facebook, they have server all over the world to reduce the latency time (and also to provide several other advantages) and they use huge caching system to cache their hot data (trending topics) whereas cold data (old data) are stored in hard disk so it takes a longer time to load an older photo or post. So, a user might would have complained about this as they were trying load up some cold data.

Since you already said when you check the site yourself the speed is fine, this means that (at least for the pages you checked) there is nothing wrong with the server and it can serve those pages at a good speed. What you should be figuring out at this point is what the difference is between you and the user that reports your site is slow. It might be a lot of different things:

• Is the user using a slow network connection (mobile for example)?
• Does the user experience the same problems with other websites hosted at the same webhoster? If so, this could indicate a network problem. Normally this could also indicate a resource problem at the webserver, but in that case the site would also be slow for you.
• If neither of the above leads to an answer, you could assume that the connection to the server and the server itself are fine. This means the problem must be in the users device. Find out which browser/OS he uses and try to replicate the problem. If that fails find out if he uses any antivirus or similar software that might cause problems.