The first couple of days after you quit are the hardest to deal with. It gets easier as time goes on, but the first 72 hours are the absolute hardest. Luckily, if you know what to expect, it makes it easier to cope with.
Why 72 hours? It takes about that long for your body to completely stop the effects of nicotine. While there are still traces of nicotine in your blood after 72 hours, it has stopped affecting you at this point.
As the nicotine levels in your blood decrease, you will begin to experience the physical symptoms that come from nicotine withdrawal. Irritability and cold symptoms are the most noticeable, but there are a few others that generally will not be noticed unless you're looking for them.
The irritability and general lack of patience will be the most noticeable. You may notice yourself less able to concentrate, and more likely to snap at friends and colleagues. Explain to them beforehand that you're quitting smoking and what to expect.
On the third day, cravings will be at their worst. You will generally experience frequent cravings for cigarettes, and it may take completely over your thoughts and cause you to be completely unable to work, thinking that smoking will make you able to think once again. This is the way that cigarettes keep you hooked, by making you believe that you need them to function.
Keep pushing through it, and your mind will slowly realize that it does not actually need cigarettes to keep working. As time goes on, you will feel fewer and fewer cravings, and will be able to function better.