Here are some resources that can get you started:
HTML5 Supports App Caching, and it works at least on iOS and I think more modern android phones as well. http://www.html5rocks.com/en/tutorials/appcache/beginner/
On iOS at least there are special meta-tags you can use in your html to make the page savable to the launch screen.
<meta name="apple-mobile-web-app-capable" content="yes">
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent">
So you can look up how to best use those.
Those things should point you in the right direction, but keep in mind that anything stored for offline use needs to be small and efficient since there is usually a limit to the amount of data that can be stored offline. Also, some browsers require that the user grant permission before any data can be saved, but the request dialog is sometimes intimidating. (e.g. "This web page wants to save data on your computer without your knowledge, do you want to let it do that?")