Dear <company name>,

My name is <NAME>. I'm a 22 year old student at <specific College>, studying both Computer Science and Game Design. I am interested in interning with your company for 3 months, but may be available for a longer period if necessary.

I have experience working in <languages: C, C++, Java>, and have particularly focused on <areas of interest: Pathfinding, AI, etc>. In our last lab course, I was responsible for <X notable thing you've done at school>.

I was drawn to your company because of your work on <Y>. I'm very interested in <Z technology>. I feel that my experience working with <something related> would allow me to quickly adapt to <Z technology>. I would also love to work in other areas, such as GUI, backend systems, engine optimization, or netcode.

I am available for a phone interview (or "face-to-face" interview via Skype) during <your hours of availability>. You may also email me at my@email.com to arrange another interview time.

Please find attached my photo and CV. My portfolio is available at <your website>. 

If anything requires clarification, don't hesitate to contact me. I look forward to hearing from you.

Sincerely,

John Doe  <Your name>
Phone: 5 555 555-555 <Your phone number>
Email: John.doe@University.edu <Your email>
Skype: JohnDoe111 <Your skype>
Linked-In: <Your linked-in>