Some spices in Greek seasoning are basil, Greek oregano and rosemary. These are spices that grow well in the hot, Mediterranean climate of Greece.
Basil is one of the most popular herbs used in cooking. It has a warm fragrance and is spicy to eat when fresh. It is an annual, which means basil only grows for one season, and is intolerant of frost. Basil is grown easily from seed but needs to be planted well after the last threat of frost. It needs lots of water and is a fairly heavy feeder.
Greek oregano is also easy to grow from seeds and will even do well in fairly poor soil, even though it needs to be in warm soil with good drainage. It is a perennial in southern climates, but north of zone 5, it needs to be brought indoors for the winter, or covered up with mulch.
Rosemary is not only an herb, but it can grow large and bushy enough to serve as a shrub. It has blue flowers, needle-like leaves and a distinct, resin smell. Like basil and Greek oregano, it does best if it's planted after the frost, in well-drained soil that's at least 70 degrees Fahrenheit.