Most schools are closed in August since this is when most Greeks take their vacation, so I'm not sure why some sites recommend that. Ads recruiting English teachers started in May and the good positions are filled before August. Sometimes, there are a few positions leftover even in September.
Some jobs require both experience and a certification. sometimes only speaking English is enough. If you're a non-EU citizen of no Greek origin, you'll have to compete with Greek and EU citizens who are legally ready to work, then find someone to sponsor your residence/work permit. The other way is to work illegally and sacrifice a proper contract with a good salary, IKA (health insurance), bonuses (summer, Christmas, Easter) and the right to collect unemployment should you be fired. Some places offer a salary, accommodations (usually on an island), etc.
Schools in remote areas or islands may also take someone without a work permit, certification or experience.
