For those of you with no contacts or networks to get your name known, then you must cultivate them. Sending CVs out will not get you a job these days. I don't know how many students are finishing each month, but I'd guess it is well over 100 per month from British schools alone.
For those still in flight training, then I second the point made earlier in the thread; be the best student you can be. I went to PAT, and was recommended to my current job. Without it, I would have had nothing, despite filling out loads of application forms and making phone calls. A simple word in the right ear works wonders. And if you get the reputation at your flight school as a lazy arrogant idiot, then you won't get a recommendation.
Still, there are people I know who three years after leaving still have nothing. It's pretty tough going, and I don't think it is going to get any easier for people with the looming recession and certain airlines only taking from certain schools. Have a plan B...