I have a landing page and I want to see how many of the people who sees the page clicks a certain button.
Say that the button has an event label, e.g. "foo". How do I find out what the percentage of visitors to the page clicks the button?
There are two methods:-
In order to obtain the % of users that either did or didn't do something on your page, you need to set 'something' up as a goal.
You'll need to set the URL of the page that contains the button as a required step and then you'll be able to see a funnel of all visits to the page that resulted in a goal (reaching the URL the button goes to).
just a note of caution: events with page-changing buttons/links can get biased a lot. it's a race between the browser killing the page view (its javascript)_ and GA registering the event. so the "completed" number may be way off. I've seen up to 50% missed on form submits.
solution: using a event with callback + preventdefault handler
check this for more (and still evolving history of the problem): https://stackoverflow.com/questions/4086587/track-event-in-google-analytics-upon-clicking-form-submit