Most useful javascript design patterns for a single page application that updates with AJAX?

For a beginner (and hobbyist) who is well self-schooled in HTML and CSS and is moderately familiar with JavaScript which design patterns should he learn and apply? My task is to create a single page application without using any libraries or frameworks. It would be a simple site that updates content only in sections of the page as they are clicked. Although it would be a one page web the address bar as well as a menu would mimick a multi-page website. It will not be built as a mobile phone app but may be accessible via one as all web sites are. The goal is use this as learning experience while building an online portolio. It would likely be hosted at Github Pages which permits AJAX updates. Please advise.