If you have an application that runs only on cell phones, you shouldn't be worrying about different screen sizes. Have you used layouts in Qt or any other UI toolkit? UIs on Android work in a similar way. Android will properly scale your UI to different screen sizes, just like a Qt window can be resized without crapping up its layout.
About graphics: Google defines 4 screen densities: XHDPI, HDPI, MDPI and LDPI. You create separate graphics for each of them and import them into your project. Android will automatically pick the appropriate version of your artwork depending on the device your app is running on. No manual work required.
E.g,
<LinearLayout
android:orientation="vertical"
android:layout_width="fill_parent"
android:layout_height="fill_parent"
android:background="@drawable/slate">
</LinearLayout>
See that @drawable/slate in there? Android will try to find the appropriate version of "slate.jpg" (or "slate.png", or whatever) from one of these directories: res/drawable-hdpi, res/drawable-mdpi or res/drawable-ldpi. If it can't, it'll try to look for the file in res/drawable[1]. So you have 3 versions of the file residing in 3 separate directories.
Don't worry about screen sizes. They don't vary too much anyway. Phones these days lie somewhere between the 3" to 5" spectrum. Not much of a difference for most apps, unless your UI is doing something very special.
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[1] This is the default project structure; you can probably change it.