(Disclaimer: advice based on what people in Finland tell people looking for a job. There may be some cultural differences, though I do think this applies relatively universally.)

A piece of advice I frequently hear: always make sure you call somebody in the company you're applying for. The recruiters will get too many resumes online to do much more than skim them through, and you have little chance of being noticed that way. You need to do something to make sure somebody actually takes notice of you. Actually talking on the phone with someone is a good way of achieving that.

It's not hard to come up with some reasonable-sounding excuse for making the call. Maybe the job ad was sparse on detail and you have some specific questions about it. Or maybe you're going to go by the honest route: "I saw your job ad and thought I would apply online. But I figured my resume would go unnoticed among all the others you get, and I know I'm the right person for the job, so I thought I'd call you and give you a heads-up that it's worth your time to take a closer look at mine." That's memorable, and shows that you have guts and confidence in yourself. Yes, it might also sound arrogant and turn some people off, but what do you have to lose? Unless your stand out somehow, you probably won't get the job anyway.

Don't just stick to job ads, either. Look for companies you'd like to work in and call people to ask if they'd happen to have use for someone like you. The rule of thumb I was given: for a company employing less than a hundred people, call the chief of the company. For the boss of a small company, somebody going to the effort of calling them and asking if they might have a job opportunity is like someone complimenting them on their children. If the company employs more than a hundred people, figure out someone who has something to do with personnel hires and call them. Say, "if I sent you my resume, would you have the time to take a look at it?". Not "may I send my resume", but "would you look at it if I did". Offer to call them back in a week when they've had the time to take a look, and then call them in a week as agreed. Make sure you call them exactly when agreed to, or if you for some reason can't make it and have to call them later, make sure to apologize.

Here's a story someone from a recruiting firm told me. A guy needed to get a new job, so he went around calling the bosses of various companies. One of the bosses said he didn't think their company would have a need for someone like that, but he'd take a look at the resume anyway. A week later, the job-seeker calls back as agreed. The boss says, "like I thought, we didn't have a need for a guy like you. But you know what? I was talking with my wife this morning, and it turns out that you are just what they need in the company she works for." He'd have gotten a job that way, but by calling various people he ended up getting an even better offer from somewhere else. I think the numbers went something like, he called a hundred companies, eighty of them agreed to take a look at his resume, twenty called him in for an interview, and maybe five offered him a job.