Some of the rules and procedures for applying for a job haven't changed in a century. You put together a resumé listing your jobs and achievements in chronological order, write a cover letter explaining why your resume makes you so ideal for the job, and you send it to the Chief Pilot or HR manager. Once upon a time you mailed these things on paper. When I started my career, postage was a serious job search expense. The purpose of the cover letter was so that when the employer opened the envelope and withdrew two sheets of paper, the top one explained who you were, what job you were applying for and why you were especially suited for the job and the one underneath, the one it was covering listed your experience.
You can also fax your resume (and could then too), but I wanted it to look nice, not depend on the quality of the destination fax machine paper and ink for my professional appearance. Hand delivering is a good option, because you often are allowed a moment to meet the person who might hire you. You can hand-deliver local resumés, or go on a road trip and hand deliver them to more remote operations. It usually makes a positive impression if you go in person to a remote place. If they have a job suitable for your experience and you are right there in front of them asking for the job, they'll rarely call in someone from far away. For remote (and for the most part I mean gravel road or fly-in remote) operations that is the best way to get the job.
For most other operations, nowadays you e-mail the resume and cover letter as attachments. There's usually a page linked from "Careers" in small print on the company website that gives you the requirements and the e-mail address to send resumés. Depending on the operation it may be better to bypass HR and send your resumé directly to a management pilot, whose name and e-mail you have obtained from a friend. When you e-mail your resume, make sure you use a subject line that makes them likely to open your e-mail. "Resumé" is better than a blank subject line, but not by much. Your name is already in the header. (At least the name associated with an e-mail account you make job applications from had better not be "c00lpIl0t1973.") It would be best is the e-mail address itself had your real name. At minimum it shouldn't be someone else's name or anything offensive. So something like "Pilot: 2000 TT, 500 on DHC3" where the operation in question flies Beavers.
So you have the cover letter all nicely formatted in Word but then you have to write something in the e-mail too, to induce them to open it. So the cover letter has a cover letter. You might say why bother, just write the cover letter in the e-mail, then attach the resumé. Sometimes I do that. But sometimes the ad specifically requests a resumé and cover letter, and you know they're going to be printed off and passed around the table. You don't want to be the one with the e-mail headers and formatting all over her cover letter.
I always try to get a picture of how this works, from what I know about the operation. Is the resume going to a non-pilot HR screener? I imagine someone opening the e-mail, based on the size and type of operation. Is this a dedicated HR mailbox? The CP going through his e-mail between flights? Someone in the customer service office sorting e-mail enquiries about charters? Sometimes I put the resume and cover letter in one document that will be printed off together. Sometimes I copy the exact text of the cover letter into the e-mail. Sometimes I put two lines in the e-mail telling them my hours, ATPL and what position I am applying for.
I go through phases where I agonize way too much about this. I know that I spelled experience wrong on the cover letter that got me my first job. I only noticed a year later when I opened the file to edit it into a new cover letter. I wonder what the heck I thought I had experienced then anyway. I don't dare to open that file now and suffer the embarrassment of seeing my past self boasting about "My 215 hours flying expereince."
But now I send off resumes and imagine that the only reason the CP doesn't phone and offer the job immediately is that he is stunned by how perfect I am for the job.