How to use AJAX to retrieve data from an external API from the frontend in Wordpress?

I am a newbie and basically I need to make a plugin that displays events on my site. I will be using an external API (eventful) to retrieve the events, and will need to do so in javascript.

I want to provide visitors to the site with a few options checkboxes which give them choices determining which events are displayed: the idea is that the option checked will change the query provided to the API and alter the events being displayed to the visitor? Would anyone perhaps be able to point me in the right direction?

via Chebli Mohamed