The best way to keep Asian make-up from going horribly wrong is to make sure that you pick the right colors and the right products. With your skin, you want to make sure that the foundation matches your skin tone.
With Asian complexions, they typically have a yellow undertone, so you want to make sure your foundation and your concealer, your powder, all match that. You also want to think about things like eyeliner.
If you have a very hooded eye, then eye shadow, cream eyeliner, cream eye shadows might run on you, so perhaps you want to look at waterproof products or gel liners that have staying powder. On your eyes, if you have a very hooded eyelid, then you might want to think about getting products that have a waterproof consistency or a long-lasting wear so that when you put it on, it stays all day. Gel liner or waterproof mascara, those are all things to consider when you're shopping for make-up.