I respond to internship requests on a daily basis. Many of the requests are one-sided and offer no benefit to the studio. Here's the deal, an internship is beneficial to both the studio and the intern. If you want to intern at a studio, you have to possess some sort of value to the progress of the studio. The studio is going to give you experience and education so you can be a competent member of the industry. If you have nothing to give back, you'll never get an internship.
Before you go and start pestering studios, you need to do a little prep work. Start with reading a few books on Pro Tools and recording principles. You can read books on many different topics and learn quite a bit about the industry at your own pace. Educating yourself adds so much worth to your assistance in the studio. Once you know the difference between XLR & AES cables, you will move quickly through patching and studio setup.
Buy some gear and do some home recordings. Get a little bit of experience with using a DAW and play around with the settings. If you want to learn Pro Tools, go to www.avid.com and sign up to receive Pro Tools First. It's a free version of Pro Tools that will get you started. Most professional studios use Pro Tools HD, so there will be a slight learning curve, but getting familiar with the fundamentals is important.
Watch a few videos on YouTube and ask some questions in forums. Do not show up to the studio with a bunch of questions. When you're in the studio, just observe! You're there to learn and the engineer is there to work. If clients are on the studio, keep your yapper shut. If someone asks you a question, answer them, but that should be the only time you speak.
If you do have questions during a session, write them down and save them for after the client's session. It all boils down to manners and common courtesy. You need experience and that is what you should absorb. Being in the room while a session is happening is chalk full of experience. Pay attention to how the engineer conducts the session. Keep track of how many takes are recorded and how they're recorded. When the session is over, start to help with the break down. Ask the musicians if they want help loading their gear. Be helpful and it will be rewarded.