Can you elaborate? Are you asking about Plataea, Salamis, or Marathon? Or the Greeks' arms and tactics, and weaknesses and mistakes made in the invasions? This is a huge question the way you've phrased it, there are entire books answering that question in the general sense.

This is a very vague question. So I can really only give a vague answer.

Depending on the battles, only some of these may apply. But essentially through a mixture of luck, superior generalship, knowledge of the local terrain, better armed infantry, more motivated troops due to fighting to defend their home, no language barriers between their troops, civil strife elsewhere in the Persian empire and the most important aspect of all that really explains the previous point - the Persian empire was huge. The Greeks were a minor annoyance that were really on the periphery of the Persians.