As louie said ... W3Schools is the place to start I think.
Web design in my mind is about having an interest and a passion in learning and finding out new things.
My advice would be to set yourself a goal and go from there. To be honest web design includes graphics / html / css / databases / programming /
SEO (search engine optimization) / javascript / AJAX / Flash / Server Admin ... and more ... . Personally I'd like to think I'm pretty good with most of those things.
My advice as I said would be to set yourself a goal also decide what do you want to know break it into chunks and go from there.
Lets say you want to make a basic webpage ... for this you'll need HTML
find out about HTML
HTML Tutorial ... once you've got a bit of knowledge about all this and can put together a webpage (I'd advice steering clear of WYSIWYG ... what you see if what you get style editors ... you've no doubt heard of dreamweaver that is one)
Once you've got your webpage together .. you might want to take a look at CSS (Cascading Style Sheets) ... this will allow you to do a lot more with you pages in terms of appearance.
Depending on who you are approaching for your lessons you'll find some charging more than others ... €20 - €30 sounds to me like a rate for grinds on an 1 on 1 basis. Given than anyone who knows all of the above is charging a lot more to design websites ... you may find yourself getting someone who is not that experienced ... again you might find someone who is a great teacher.
There are alternatives and those would be online courses ... you might find Lynda.com to be a great place ... it offers video tutorials about everything. A lot of webdesign is doing things ... you can have your teacher teach you a lot in an hour but unless you go and put it all into practice you are probably kidding yourself.
Anyways ... goodluck with the "career" choice
James