Discuss about your and employer's expectations for the internship. It is advisable to agree upon your job responsibilities in writing.
Meet your supervisor regularly to ensure that both of your expectations are being met. This is a great way for getting feedback on your performance and keeping you on track with current and future assignments.
Be observant and ask questions about the company's culture. Different organizations have different expectations regarding employee behavior and it is important that you learn about and conform to the corporate culture. This can include issues such as appropriate clothing, demeanor with customers, personal phone calls and where to park your car.
Focus on your verbal and written communication skills. Proofread your written work carefully. When communicating with your coworkers choose respectful, tactful and professional language at all times.
Show up to work on time. Inform your supervisor if are sick or going to be late. Choose your sick days carefully; it will be noticed if you are not at work on important days.
Establish good relationships with your coworkers. Be friendly, polite and helpful towards your colleagues. Be careful about bringing personal business to work and discussing what is fit for public consumption.
Be flexible to work with. Learn to work as a team; be respectful of input from other team members and practice the art of compromising.
When you leave, request your supervisor for a letter of recommendation and keep in touch so that you can call upon him/her later when you are in need of a reference. This will help in registering yourself in your supervisor's mind for future opportunities.