Without a doubt the best answer to this question is:
Buy and read this book: http://www.amazon.com/Beginning-Android-Games-Mario-Zechner/dp/1430230428
It was written by the author of LibGDX which is one of the most popular android game engines. The book teaches you everything you need to know to build a complete game.
I can't say anything about the 'best' way, but you can use
OpenGL ES 1.0/1.1/2.0, or
Draw to a Canvas or View.
Beginning Android Games is probably the single best resource (especially chapters 3&4). You should also look at the SDK samples (snake, lunar lander). Practical Android 4 Games Development is... not good (the copyediting is particularly shameful), but it is at least devoted to game development with OpenGL ES.
I have Beginning Android Games by one of the guys behind libgdx. I found it really easy to work through. It covers 2d game programming pretty well and even gets into some of the basic open gl stuff.
It gave me enough knowledge to branch off and start a project of my own with confidence.
You can start using the official resources:
2 Great books from Pragmatic Bookshelf:
Google should be your best friend.
Getting started with OpenGL... in Android
Pro Android Games
Beginning Android Games
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