Cross your 't's and dot your 'i's
Don't send a resume without a cover letter. Don't make the reader guess what you are asking for; be specific: Do you want a summer internship opportunity, or a permanent position at graduation; are you inquiring about future employment possibilities?
A flyer posted in your department, a web site, a family friend who works at the organization. It is appropriate to mention the name of someone who suggested that you write.
The cover letter will be seen first. Therefore, it must be very well written and targeted to that employer.
Education, leadership, experience - that are relevant to a position you are seeking. Be as specific as possible, using examples.
Personality, motivation, enthusiasm, and communication skills.
In a job advertisement that might not be covered in your resume, such as availability date, or reference to an attached writing sample.
Applying for an advertised opening - applicants often say something like "I look forward to hearing from you." However, if you have further contact info (e.g. phone number) and if the employer hasn't said "no phone calls," it's better to take the initiative to follow-up, saying something like, "I will contact you in the next two weeks to see if you require any additional information regarding my qualifications."
Asking about the possibility of an opening - don't assume the employer will contact you. You should say something like, "I will contact you in two weeks to learn more about upcoming employment opportunities with (name of organization)." Then mark your calendar to make the call.