A cover letter is the employer's introduction to you and what you can do for the company. Before even looking at your resume, the employer wants to see that you can present yourself well in writing and that you have carefully considered why you want the particular position for which you are applying. Take your cover letter seriously, and avoid copying and pasting information from one to another for each job.
How can you customize it? First, avoid making obvious errors, such as forgetting to change the job title, hiring manager's name, date, and the name of the company when you bring up your cover letter template on your computer. Carefully look through the entire document to be sure that you have all of the little details right before you send it out. Take a break from the cover letter for a couple hours before you send it so that you have fresh eyes to spot any such mistakes.
Additionally, tailor examples of how you meet the skill requirements listed in the job description. If you are applying for a first grade teacher job, for example, and you use an English as a second language teacher cover letter that you used last month, it may not be relevant that you are familiar with your state's ESL yearly testing requirements. Instead, you should focus on that you know how to create project-based units for science that meet Common Core requirements for first grade.
Writing a cover letter should be done with care. It is not something that should take you just ten minutes to complete. Carefully read through the job description. Highlight your skills that match those that it lists. Use numbers and percentages in your examples of how you meet those skills, and then mention how you can uniquely fill the organization's larger goals.
If possible, have someone else read through the job description, look at the organization's website, read the biography of the hiring manager on the site, and then read through your cover letter to uncover any glaring mistakes you made or to perhaps suggest a different angle from which to present yourself.