Over the past couple of months, a few people have asked me for advice on this. I don't have the magic formula but I do think there are some things you can do over and above the standard things, like tailoring your resume to the job announcement.
1. Ask A Mentor
Ask someone to help you out, to give you advice either regularly or periodically. Join a mentor-mentee program. Most people would be honored to do this as long as it's not too big of a time commitment. You can have more than one. Remember to return the favor.
2. Volunteering & Professional Industry Activities
You want to show that you add value. You are driven to add value, and will find a way to do it no matter where you are - working independently and together. You can volunteer for a charity, join an industry group, start a group, and so on. By doing this you show that you are proactive, a team player, and it helps you gain visibility in your area of expertise.
If you want to stand out from other applicants, do the work first and let it speak for you. Start a project or initiative. Demo a best practice. Get your name out there. The more you do, the more you share, the more recognition you receive, the more you've proven that you are the expert and the more reason to choose you.
4. Technical Skills
Employers are generally very impressed when you show that you have a lot of technical skills. List them on your resume exhaustively. If you don't know something, train yourself using one of the free resources out there.
5. Portfolio & References
These two things go together: Build your online presence through a self-created portfolio of creative work, and endorsements for the work that you have done. There are a lot of free resources out there with which to do this. People who do this are showing that they have confidence in the work they'v done, and that others do too. It's not technically difficult at all, more emotionally challenging because most people don't like to promote themselves so baldly.
What can you spend less time on? Personally I don't think the cover letter matters all that much. It's often a lot of fluff. And if it sounds insincere, then it's actually a real turnoff.
Overall, it's a competitive world we live in and growing more competitive by the day. It is tempting to think that a host of unfair factors are holding you back. Maybe they are and maybe they aren't, but my experience is that people who are highly skilled, highly motivated, and highly literate in the process job-hunting are at an advantage.
All opinions my own. Photo by Michael Maggs via Wikipedia.