I'd like to add a simple web part to one of our pages to track the load time of the page and display it to the user. Although I thought this would be common / easy to google it doesn't appear to be the case. How can something like this be done, simply?
I've never tried this with SharePoint, but you could investigate the following functionality:
Taken from http://stackoverflow.com/a/2818117, pertaining to ASP.NET.
You could turn on Trace. There you will get a bunch of information about the Page lifecycle( including time stamps), and other useful profiling information.
Turn on trace for a page in the Page directive at the top of your aspx file:
Or dynamically in code:
Or globally in the app setting this in web.config: