Make a list of company's of where you would like to work, and or the leaders who you you resonate with. Follow the individuals on Twitter & LinkedIn, set up Google alerts for the company that will send you across information on what is happening. You need to promote yourself by creating a one pager on yourself. Break it into segments of what you are studying; your strengths; list awards, accomplishments, and areas that you would like to work in. Keep it really concise...have a look at this by Marissa Mayer CEO Yahoo to get an idea of what I am suggesting, obviously make the headings appropriate to reflect you.
I also like to include a quote that represents my values and or work ethics.
Keep refining this and make sure you have it with you on any occasion or are sending it to any company's or work opportunities.
When you are then communicating or meeting with the company spend some time on sharing what you know or admire that the company or doing. It could be there community efforts, their values, a new product, a charity that are aligned with etc.
Sara Beth’s Answer
You can sell yourself to a company with a lot of tools. The first thing is getting your resume up to the mark!!
Yes-Sell your self to the company with your Resume!! Your resume does the work for you in securing an interview. That's like the first 40% of the work in getting you your job. Research how other people make their resumes with that profession. Its easy to see resumes of different people these days as its available to view for free on Indeed--> Find Resumes. Have your resumes reviewed by some experienced people within your profession of choice.
Secondly, Network with your linked in profile--Add key words to your linkedIn profile that are relevant to your profile. Jargon that will get you noticed. Connect with people who are working in that company. Primarily Network with them.