Plastic: This is a favorite trick because wrinkles are caused by friction. You will need to pack all your clothes in individual plastic bags or some that came from your dry cleaners. Best option for suits, silk, and other fine wear.
Military fold: This is a favorite because it also allows you to pack more. Fold in three the long way, then roll from the bottom. Great for pants, shorts, T-shirts, and some shirts.
Wrinkle free spray: Just spray it on the clothers, wait maybe ten seconds, smooth out the garment and your wrinkles will be history. Good for Dress shirts, but follow the directions.
Pack wrinkle free clothing: If at all possible this will save you lots of time. Buy clothing that has wrinkle guard already built in. This does not work on suits, but for regular clothes this is good.
Mesh bags: This is great for delicate items such as lingerie. It has the added advantage of being see through so airline inspectors won't need to rummage through them.