Greek god costumes start with either a chiton or a toga. The chiton is the classic Greek outfit, while the toga was its Roman counterpart. Both are absolutely acceptable, though the former is marginally more accurate. From there, you can garnish it with a few basic accessories, along with details specific to the god you wish to portray. All of it can be done with basic household items and a little arts and crafts know-how.
Measure a length of muslin cloth the same height as you are and the width of your outstretched arms.
Fold the top 45 cm (18 inches) of the fabric down to make a drape.
Fold the fabric in half and sew the two ends together with a needle and thread. You should be left with a circular tube of fabric.
Use a broach or safety pins to pin the top of the tube together. The pins should be a few centimetres from the ends of the tube, enough to give your arms room to slip through. Women should use two pins or broaches. Men should use just one -- the one corresponding to their left shoulder -- and let the right shoulder drape free.
Slide yourself into the tube and make sure the broach is secure.
Wrap 3.6 to 4.8 m (12 to 16 feet) of cotton or muslin cloth around your body. The fabric should be about 90 cm to 1.5 m (3 to 5 feet) wide. You want it to hang down to about your knees. Men should wrap it around their waists, women just below their armpits. Wrap it around your body at least 1 1/2 times, though you can wrap it more times than that if you like.
Pin the wrappings at your waist or below your shoulder blades, using safety pins or hairgrips to secure it in place.
Throw the excess fabric over your shoulder and down your back. Pull it in front of you and pin it to your waist again.
Wrap a belt around your waist to secure your chiton or toga if you wish (it's not necessary, but it provides an additional level of support). Substitute a belt for rope made of gold or silver fabric if you really want that Greek god look.
Wear sandals, the only accepted footwear on Mount Olympus.
Wrap a wire coat hanger around your head, just above the ears. Remove it and then wrap plastic ivy around it to create a laurel.
Select an accessory specific to the god or goddess you are portraying. There were 13 gods in the Greek pantheon, each in charge of a single sphere. Zeus was king of the gods and hurled thunderbolts from the sky. A cardboard thunderbolt wrapped in gold foil might work well. Apollo was god of the sun, archery and music; use a bow and arrow or a Greek lyre if you can find one. His sister Artemis was goddess of the moon and the hunt; use a cardboard crescent moon or bow and arrows as well.
You can vary the colour of your fabric to taste, but you may want to associate it with the theme of your chosen god. Dionysus, for example, may wear robes or purple, since he is associated with wine. Apollo may have robes of gold or blue while Hades may have black robes corresponding to his position as lord of the underworld.