Well, first, cover letters can be important. They're your chance to express a genuine interest in the company and industry beyond simply sending them a resume. As resumes become easier to send out to many employers, simply sending one loses signal value. Doing a little research on the company in advance can be very helpful.
Ask yourself what things the company would want to see in an applicant.
What skills do they want? How does your resume demonstrate them?
If you're transitioning from a different pursuit, you'll want to couch that different pursuit in terms that demonstrate how it prepared you for your current pursuit.
If you have a gap in your employment or academic history, you'll want to address it somehow. Part of the employer's decision is the degree of risk an applicant represents. Can they count on the applicant to show up, work well with others, be conscientious about their work, etc? They'll be looking for various traits in the resume.
You want a single page resume. Use bullet points. You'll go through several drafts, and that's fine. Keep editing, keep correcting. You'll think of new things as you go along, and you'll find typographical errors and other minor things that actually can make a difference. The degree of care you show for perfecting the resume will, fair or not, reflect on you.
Remember that your resume will grow with time. Don't worry if you don't have much work experience at the moment.
If I remember correctly, you've traveled extensively overseas. I'd list this in an "Interests" section - not simply as "traveled extensively;" provide a little more color than that - because it's something many people haven't done, and indicates self-reliance, a willingness to take risks, and an ability to navigate the world generally without causing catastrophe.
