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):
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.
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: