I studied this in class this week. The incubation period for a common cold depends on the kind of virus it's caused by. The incubation period is at least two days and up to a week or two weeks depending on the cause. Some people get symptoms within the first day though.
I had a cold last month and I know that I got it from a classmate. Some mild symptoms started the day after I got the virus from him, but I was very sick only by the third day.