Being a president of 2 clubs and dealing with plenty of university bureacracy here are the steps. First, you have to find which organization is in charge or monitoring, financing and supporting all the clubs usually it is student union or something like that. Contact them and get all the neccessary paperwork.
Second, make sure you have a statement of purpose and some kind of an outline which will show how the club will operate, who will be in charge, what kind of events will be planned, how many people you think will participate, etc.
Third, a sample budget wouldn't hurt. Ask student union for help on this one or some other club officials.
Fourth, you need to lay the groundwork for club constitution, which will contain a lot of things mentioned in part 2.
I don't even know if you really need a professor to start a club. At my school you didn't. I hope you're not talking about a high school club?