There are paid an unpaid internships. Often this will depend upon the experience you have coming in and the type of organization for which you are interning.
The more experience you have, the more profitable the company you're interning for, and the more formalized an internship program they offer, the more likely it is that you'll get paid. For example, if you're a graduate student with 2-3 internships already, you're interning for an insurance company like Blue Cross or Aetna, and you're a part of their formal internship program you'll get paid. If you are a freshman in college, have no experience and only a year of college under your belt, are working for a local non-profit that doesn't have a formal internship program, you probably won't get paid.
If it's somewhere in-between like you're a 3rd year in college and working at a doctor's office, it's best to ask if they will be able to pay you and if so, how much. It doesn't have to be an awkward thing to ask. You can always put it into context and say, I just want to try and plan my finances for the year because I have to make student loan payments. If you frame it this way, people will be more understanding and won't think you're greedy or just working there for the money.