Greeks tend to eat lunch at 1.00pm at the earliest, and dinner at 9.00pm at the earliest, and much later, especially in the summer months when they love to sit out in the cool wee hours (they manage this trick by taking long naps during the hottest hours of the afternoon). But most tavernas, especially when there are likely to be tourists around, open from about 6:00pm (some never close after lunch) so if you want to eat earlier you certainly won't starve. But you may only have other foreigners as company.
Unless you go to a smart restaurant, eating out tends to be extremely informal. You sit down, the server whips out a paper tablecloth and fastens it over the table (on islands, these paper tablecloths often feature useful maps); they are there for hygiene and to save money and energy washing tablecloths. Someone will plop a basket with napkins and cutlery on the table for you to pass around, usually with some bread to nibble. In touristy places they may also plop down a bottle of mineral water (which you will be charged for); if you don't want it and prefer tap water, ask for νερό από τη βρύση (nero ap ti vrissi).
Image by Andy Montgomery