There's no single answer to this - it's a broad topic.
One thing to keep in mind before you start, is that there's currently a lot of code floating around the web that assumes you can judge a screen size by the platform version: IE, everything up to Gingerbread is a phone, and Honeycomb (and up) is a tablet. This is a bad idea. Don't do this :) Also try to avoid a massive switch case that just executes different blocks of code based on width/height values you pull from the system. I'm not going to describe how to do that, others have already given that answer.
One thing to investigate is the Android Compatibility Package - It lets you use Fragments and Loaders (which were introduced in Honeycomb) in earlier versions of the Android platform. One common pattern this enables is to let you set up a nav fragment & content fragment which sit side-by-side on a Tablet (where there's room) but have the nav fragment switch over to the content fragment when an item is selected on a phone or smaller screen.
If you're just trying to have images that grow and shrink with screen size (that you're not drawing programmatically), the answer is 9-patches.
You also have the option, if it's appropriate for your application, of using Android Market's Multiple APK support. The linked page dives into how to set that up, and gives you a pretty solid description of when to use it and when you're better off with a single APK.
