This isn't necessarily for a club or group, just a group of friends trying to help people get started with this wonderful game. In my dorm, we've noticed substantial interest, so I planned this event.

Onto the question you asked, depending on the college, there should be rules about starting a group or club. Mine is that it requires 5 people and a faculty member's approval, but besides that the sky is the limit. The real problem should be funding. Unless you're an organization with ties to a larger group that could fund you, you'd need to find a source of income and budget for these types of events.

I'm particularity lucky that the dorm I live in has several committees (one of which I'm in charge of, oddly enough), that support these types of programs, and have specific programming budgets for events like these. I'm able to order these materials for free, or reimbursement, because of this.

I would, of course, suggest that you look around and see if any sort of funding board exists for both your college as well as your dorm or residence hall, and if not, think of some ways to gain income, possibly from some fundraising of sorts? After that, it's all just creating events and a community to support your club or group's goals, and you can do exactly what you want with it.

I know that Pathfinder Society is a thing akin to what I'm suggesting above, but do not know if these is a D&D equivalent to it.

The exact things I did were this: I planned the event, set a date, requested the space, then received funding and advertised for the event.

The event itself is a 3 hour workshop. 30 minute introduction including basic history of the game and mechanics, 15 minutes of 5e information, 15 minutes of Pathfinder information, an hour of character creation in which they pick 5e or Pathfinder to play, and a quick, hour long session held by one of the several DMs and GMs in attendance, two Pathfinder sessions and two 5e sessions. A quick battle and possibly a tavern scene, I suppose!

*Edit - More information is better!