As students, there are a lot of opportunities to get experience and increase your network that might not be so obvious. I am a big proponent of working events that aren't full blown, several month long internships. You can gain a lot of experience from events that may only be a week or even a few days. Students should do some research and see what events are happening in the area where they live or where they may have family that they can stay with during spring break or winter break. It's generally pretty easy to volunteer for these events. Students can sign up as a general volunteer or even take the next step up. In that next step, students contact the organization, let them know that they will be in the area, send in their resume, and ask if they can volunteer to work the event for one of their areas.
For example, if a student lives in Atlanta, he could volunteer to work the ACC Basketball Tournament. Check the ACC website to find the name(s) of the person in charge of the tournament. Send that person a well-written cover letter and resume well in advance of the tournament. Let him/her know you're going to be in the area and that you're available to volunteer. If you can't volunteer through the ACC, check with the Atlanta Sports Council to see if they need volunteers, whether serving as a greeter at a host hotel or working transportation or some other area.
These types of events give you great insight into how different events and their specific pieces work. It also introduces you to new people from whom you can learn a lot just by being around them and having conversations with them. Give it a try. This is how I started my relationship with the ING New York City Marathon. Eight years later I'm still working with them.