Just as Dirk says you can use Analytics. But... dependent on GA version (classic/universal) you can add this in tracking code:
_gaq.push(['_setSampleRate', '100']);
_gaq.push(['_setSiteSpeedSampleRate', 100]);
and for UA code is:
ga('create', 'UA-XXXX-Y', {'sampleRate': 100});
Please note - for classic you can put code after initialization and before track page view. For UA you need to change way of initialization to include this sampleRate. Then you can go in GA -> Behavior -> SiteSpeed and will get speed data for about 100% of visits.
Later - use PageSpeed Insights to track speed of pages. If you're in WordPress you can use plugin:
http://mattkeys.me/products/google-pagespeed-insights/
and check score of all pages/posts. There is free version, just scroll to bottom.
After you can use Pingdom Tools, GTMetrix and WebPageTest to see how your site is loading on different geolocations, browsers and connection speed. All of tools give some scores and suggest improvements, just follow their suggestions for better performance.
And if you are willing to get even higher speed improvements you need to read least two books:
So both books are amazing and completing each other. First explaining server performance, network performance, some specific improvements about browser core, etc. Second book is explaining how to clean up actual site for better performance - minimizing and cleaning CSS, selecting best images, JS improvements, HTML tricks, etc.
After you reading that books and using tools you can optimize site slashing minimum 50% of it's footprint.