I have read in a DC comic about John Constantine where the superhero says that ultimate secret of magic is that anybody can do it. However, I don't believe I have ever read a DC comic that reveals any public available method for learning magic that's accessible to the average person. Is there any DC comic that shows a public available method for the average Joe to learn magic (ie. book in the library, lessons anyone can pay money to receive, etc.)?
Anyone in the DC universe can learn magic, yes. But for humans it takes a special gene in order to be able to use it without the aid of magical items or pacts with magical entities.
People with such genetics belong to the Homo magi subspecies. This was shown for the first time in JLA #165, from 1979 (as seen in the link).
Homo Magi are naturally adept at magic; since many humans possesses the Homo Magi gene because of their relationships in the distant past, these humans can learn to use indirect magic by performing rituals, but pure Homo Magi or their direct descendants can use direct magic.
I think whomever wrote that left out a word. It should read "(...) but only pure Homo magi or their direct descendants (...)".
Please notice that since DC has rebooted their universe a few times since 1979, so that may not be the rule for now. I am so old that I know who the Wonder Twins are, and I haven't checked much of the latest stuff.