An omikuji is a strip of paper with fortunes written upon it. You never know what's written inside, because it's all mixed up randomly. There's usually a box or a cylinder shaped box that one needs to shake and a chest with numbers written on each drawer. By shaking, a wooden stick from the bottom of the box slides out with a number on it. Then, you look for the drawer with that number written on it. Inside, will be your "omikuji" and it will have your fortune written on it.
There are usually seven results. They are:
Dai-kichi - excellent luck - The best result, great blessings.
Chu-kichi - Fair luck - Not the best but good enough.
Sho-kichi - Small luck - Could be better but you might bump into something nice. Rate definitely goes up.
Kichi - Blessing - Life may be normal yet there might be something special.
Sue-kichi - Near-blessing - Cloud be pretty close, but not good enough yet.
Kyo Cursed, bad luck - Not a great omikuji to pull out on New Year's or before promotion.
Dai-kyo Great curse, great disaster, the worst - If you pull this one out, I'd consider buying a life insurance policy ASAP.
If you pull out something nice like dai-kichi or chu-kichi, you could take the omikuji strip with you. It is said that the omikuji paper will protect you from bad spirits and lead you to the good way. But if you pull out something bad, or a result you are not very happy with, then you tie it around the pine tree in the shrine. In Japan it is said that by pinning the unluckiness onto the pine tree, the spirits will stay there and won't come near you.
Comparing your results with friends or family is always fun too. It's part of the omikuji's fun to predict each other's year and how it will go.