how does one identify why a website is slow?

I was asked this question once at an interview:

"Suppose you own a website where the server is at some remote location. One day, some user calls/emails you saying the site is abominably slow. How would you identify why the site is slow? Also, when you check the website yourself as any user would (using your browser), the site behaves just fine."

I could think of only one thing (which was shot down):

Check the server logs to analyse incoming traffic. Maybe a DoS attack or exceptionally high traffic. Interviewer told me to assume the server has normal traffic and no DoS.

I was kind of lost because I had never thought of this problem. I have almost no idea how running a server/website works. So if someone could highlight a few approaches, it would be nice.

While googling around, I could find only this relevant, wonderful article. That article is kind of too technical for me now, but I'm slowly breaking it down and understanding it.

Solution

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.