It's too big a scope to answer here.
You should mainly consider the UI/ sizing of the elements on your page. There are a handful ways to achieve this:
But, overall, most functionality you build into your HTML5 site (if you're only using PURE HTML5 will work on your smartphones/ tablets/ desktops alike.
Following are a few sites with some valuable information you should look at:
http://mobilehtml5.org/ - Generic instructions, dos & donts, etc...
http://jquerymobile.com/ - jQuery for Mobile - it's all there for you in the box!
You could also look up on Google for Mobile HTML5 starter resources to read about it before you begin!