I'm native Romanian, fluent English and medium German. I've learned both on my own. School was terrible for learning anything.
Read, read a lot. But not hard-copy books. Read short articles. Read something you're interested in and already have some knowledge of. Technical stuff is easier than literature. No metaphors, no hidden meaning. You might not understand much in the beginning, but that's ok. If you at least get the gist of the article, you're good to go. It keeps you interested. Install the "Wiktionary and Google Translate" addon (if on Firefox, or similar for other browsers). Double-click a word to pop up it's definition. Or select whole sentences to instant-translate them. Every word definition is a click away. The more you see, the better you become.
Watch your favourite tv show with subtitles. If the tv show is in English and you already know English, that's all you need. Put on the subtitles in the language you want to learn and see the magic happen. You'll pick up words and expressions in no time. Dramas/thrillers work better than comedy. Comedy is usually fast-paced and has complicated expressions. Recommended: Dexter, Breaking Bad, SOA, etc. Not recommended: Friends, Big Bang Theory, etc. You get the idea.
It takes time, but it's better than learning all the grammar before you even have the chance to use the language. It's like learning the geometry of the hammer without ever using it. A little grammar right at the beginning might help, of course. But don't stay too long in that corner.