Timing one page loading
The crude way to measure performance of anything in Moodle is to turn on Site administration -> Development -> Debugging -> Performance info. That puts some performance stats in the footer of every page.
(You probably don't really want that. At the OU we put a little hack in the code to turn that option on when you are logged in as admin, but not otherwise.)
Note that that just shows the time taken to render the HTML, not the time that page appears to users, with all the CSS and JavaScript downloaded.
So, another approach is to use your browser's developer tools. The network tab will give you a timeline of the page loading, including all resources.
Load-testing
There are two approaches to this that I know.
The most common it to use JMeter to simulate the load. (There are other similar tools, but JMeter (https://jmeter.apache.org) is the one we & others use, and people have shared their scripts.) There is now a script-generator built into Moodle. See http://demo.moodle.net/admin/tool/generator/maketestplan.php (log in with the admin account) but as far as I can see that does not support Quiz yet. It is perfectly possible to create the JMeter script by hand. JMeter has an option to record as you go through the site in your browser. That is a good start that you then need to edit. The tricky bits are getting users logged in (use a Cookie manager and simulate completing the Moodle login form) and submitting the quiz (you need to use regexes to get the sesskey and necessary ids out of the page, so you can submit the responses.)
The other option is to to use the back-end that the Behat functional testing uses. You can use that to drive a web browser to simulate a number of users. We did that recently and I will try to share my scripts when I get a moment. (I don't have them here.)
Profiling
You did not ask about this, but once you have found something that seems much slower than it should be, profiling can be a good way to work out what the problem is, even if the problem is with your server configuration, rather than a bug in the Moodle code. See http://tjhunt.blogspot.co.uk/2013/05/performance-testing-moodle.html. Profiling will show you if the problem is Moodle spending all its time waiting for the database, or the cache back-end, etc.