Saying 'handsome' in Japanese is actually quite easy and I think there are some similarities to the English word.
ハンサム - hansamu
If you want to say it to someone ( "you're handsome") then it would be:
あなたはハンサムですね。 - Anata wa hansamu desu ne.
Here is a video that explains how to say "you're handsome" and pronounce it.
Alternatively, you could also say:
あなたは格好いいですね。- Anata wa kakkoii desu ne.
which would be more like saying "good looking".
Hope this helps!