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Connect your qualifications with the position. Be as specific as possible. Don't include information included on your resume. Write to get the interview.
If you're trying to explain your qualifications, competence, and your ability to take on jobs or projects, it's important to make those connections clear in a few sentences and explain the ways in which your experience doing other things connects to your ability to do this thing, whether it be a new position, or a transfer, or an entirely new job. Outline some of the experience that you have in the field or industry you reference in the letter. If you have targeted the introductory letter as mentioned, it will be focused on some kind of professional field or industry. It's helpful to include specific skills and experience in order to make the letter effective. Wanting a job is not the same thing as qualifying for it. If you outline in the introduction that you're interested in interviewing for the job because you'd made an excellent fit, you don't need to repeat yourself fifty times throughout. Writing that you "really really need this job" doesn't make you seem like a more attractive candidate. Set up a time that you can meet in person, or express what exactly you would like to happen next in response to your letter. If you want to discuss your qualifications further with an interview, say so. If you want the job outright, say so. Learn everything you can about the hiring process, or the application process to which you're writing, then ask for the next step in the process. Focus the introductory letter toward a specific job level. This job type or position doesn't have to be explicitly mentioned, but keep in mind what kind of result you are going after in order to keep the letter relevant. Listing out your degrees, your awards, and name-dropping in an intro letter is a bad idea. Repeating information that can be quickly glanced at on your resume is a waste of space in the letter. You're not trying to write about information that can be gleaned more quickly and easily elsewhere. You're writing to sell yourself and to get your foot in the door. It's unlikely that you're ever going to get a job or be awarded anything that you want from the strength of a letter alone. Writing the letter gets you a foot in the door, a chance to prove yourself and your ability to be the person or the employee that the reader of the letter needs. For this reason, it's good to cut to the chase, highlight your qualifications and connections to the position and try to get to the next stage in the process, whether that be an interview or some other hiring step. Reiterate the most important information in the conclusion. Just before you close the letter with an appropriate salutation, it's a good idea to briefly reiterate the thing that you want, directly.