First step is don't panic. There is petty theft like this, but you can minimize your risk by being smart-not paranoid but mindful. If you have traveled in Europe before I don't think Greece is any worse. If you haven't here are some tips
-most likely crime is pickpocketing. Not violent, you won't know it happened until you can't find your wallet. So personal safety should not be a major concern (just like at home be reasonable and don't go flashing cash in sketchy alleyways at 3AM).
-NO TO YOUR BACK POCKET. For anything including your wallet or phone. Get a front pocket wallet. Many people just carry a small amount of cash for daily expenses like snacks, admission fees, in a front wallet and have a money belt hidden under their clothes with credit cards. If you do this, the money belt is for storage only - don't access it.
-car - keep your luggage in the trunk, not visible. When you get to the site do not open the trunk - have the items you want to take with you in the main car so you can get them and lock the door. That way no thieves see that your car is full of luggage. I haven't driven in Greece, others will tell you how big a problem theft from cars is, this is just general advice.
-in general practice street smarts. Don't leave your phone on the edge of a table where a passerby could grab it. Be aware of your surroundings. Feel free to say no to people if they are bothering you or seem to be up to something. In Paris there are people who will approach you with a petition and pick your pocket while you try to figure out what they are up to. Just tell them to go away and they will find an easier mark.
-taxis - like anywhere some are good,some are bad. Best you can do is insist on the meter. In Rome there is a scam where you hand them a bill that is too big (say a 20 for an 8 fare) and either they don't have change or they convince you that you gave them a smaller bill. Be alert.