Anyone have experience with teams?
Speak to their Head Athletic Trainer (for the team and/or the University, as appropriate) first, and then also the team's Coach. Ask them their needs and expectations and inform them how you might be able to help meet those needs. They may expect you to have specific skill sets, or know how to do 5-15 minutes of extremely specific work upon command, and they will expect you to NOT exceed their directives unless given latitude to do so.
Scheduling expectations will vary from a few hours a week to daily work and traveling with the team. Consider in advance what kind of commitment you can make, and what hours you may be able to devote to working with them.
If you work with the team, would you be an employee or an independent contractor? What kind of compensation structure/rate would be provided? If this is going to work out, you need to know these things in advance.
TIP: NEVER refer to the Athletic Trainer(s) as a "trainer" - over 70% of ATCs (certified Athletic Trainers) have Masters degrees, and many have PhDs. An ATC is a licensed profession (akin to PTs, DCs, etc.) in most states, and it may be helpful to educate yourself a bit about them. ATCs are WAY more educated than the average personal trainer, and should be treated with appropriate professional respect. It is best to ALWAYS refer to them as "athletic trainer" or "ATC" - or you may blow this opportunity.