Cutting Asian hair is a challenge as compared with Caucasian hair because it's especially straight and thick. Because of this, it usually won't lay flat against the head. A normal cut with scissors doesn't always work on Asians for this reason. It's a good idea to get proper training in this specialty, but here are a few tricks to get you started.
Razor cut some layers into the hair. This gives a softer look while adding body and texture. You can add chunky layers for a more dramatic style.
Add subtle layers using thinning scissors to help it lay flatter and thin out the volume Asian hair naturally has. Use the scissors to cut layers into the hair and it will give it a less drastic layered look. You can also use the thinning scissors to make the hair look as if it's not even layered: just do this on the underside of the hair, then use straight scissors on the top visible layer.
Employ a point cut technique. Since Asian hair is so straight, it can look uneven easily, which point cutting can eliminate. It can also get rid of the "bowl cut" look when you cut their bangs.
Do a side-swept bang. This may take awhile for the client to get used to styling, but cutting a long side-swept bang will create some versatility. You can point cut this as well.
Taper the hair to frame the face. This also helps reduce the volume and make the hair more manageable for the client.