I'm unemployed and looking for a job. I have applied to all workplaces near me that I can imagine my education would be suitable. Now I'm at the point that I can't imagine who could recruit me. I'm wondering how useful would it be to learn basics of WWW-programming to make a homepage where I put my CV and tell that I'm willing to work. Would anyone take a contact via homepage?
You could potentially set up a Wordpress site which only requires minimal setup and little to no technical knowledge, however.
At the end of the day it really depends what you're trying to accomplish. Setting up a website is like opening a market stall in the middle of the forest: no one is going to know it's there unless you tell them about it, and even then, will they actually visit it? How are you going to attract traffic?
For most situations you're far better off simply creating a profile on professional networking sites such as Linkedin which are already insanely popular with recruiters and employers.
Research whether your particular industry uses one site over the other. Research what makes a profile stand out on that site. Get help rewriting your resume/cover letter, and maybe run some practice interviews with a friend or staff at a hiring agency.
If your approach isn't paying off, change it!
If there's good stuff on your homepage that makes you worth looking up for companies, and you make sure that searching for your kind of specialization ends up at your homepage, yes, certainly. This is how a lot of IT-professionals get found by companies. They have a homepage with stuff they've made, blog posts with valuable information, and some contact info and a CV. IT-recruiters will find those and will reach out to them.
But if you need to learn web programming just to make a site to put your CV on? I wouldn't count on it too much. You're more likely to get lucky putting your CV on established networking websites like LinkedIn.