The path I followed to get a decent understanding of the game (I'm about 13kyu now) was this:
1. Start by playing a few games, doesn't really matter the size of the board, or whatever, it's just for context and to get a general feel for the game. But not enough games to get dejected or fall into bad habits.
2. Read an introductory Go book. I personally first read "Go; More Than a Game" by Peter Shotwell. It explains the game from the very beginning and also has a lot of historical context which most Go books do not. My roommate had this book which was very convenient for me. An online resource that is fairly good is Sensei's Library, especially http://senseis.xmp.net/?HaengMaTutorialForBeginners. You can also find the definition and exampels of all Go terms here.
3. Play more games, try to apply things you learned from the book. Also start watching Nick Sibicky's YouTube lecture series. Just start at #1 and keep watching when you have time. I'm only on lecture ~30 but I find they have been very helpful.
4. Get a Tsumego (like chess problems, but Go problems) app or something for your phone and do a Go problem every so often. (Try to do at least 10 problems a day. Try reading it out rather than firing shots blindly. If you just brute force the solution you won't learn nearly as much as if you spend a long time just trying to read it out.)
5. At this point, you should be playing a few 19x19 games every week. Keep in mind that 9x9 is fairly different, so play it if you like it but keep in mind it is not 19x19 at all. Try to review after each game, or have your games reviewed by stronger players. There are a lot of friendly, helpful, and knowledgeable players in the chat rooms on online-go.com and the review tool is pretty cool. The site actually uses a pretty modern stack, too, using node.js and Angular, if I recall correctly... the devs hang out in chat too and are fairly open to questions)
6. At this stage, you should be somewhere around 20-15k on online-go.com. (Essentially, past the most basic novice level. You understand atari, ko, etc. You recognize some of the obvious mistakes.) Now it's time to buy a more serious Go book. I highly recommend "The Fundamentals of Go" by Toshiro Kageyama 7p and "Graded Go Problems for Beginners" (Volume 2) by Kano Yoshinori 9p. Kageyama's writing style is pretty entertaining and he stresses the fundamentals which are very important. The Go Problems book covers a lot more than life and death, it has opening, end game, etc problems, with explanations attached to all the answers.
7. Keep playing games, doing tsumego, watching youtube videos, and re-reading the books if relevant. It should be a straight and steady climb to single digit kyu-dom from here on out. At least that's my hope. :)
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NOTE: Do not play against Go computer programs if you can help it... they play bizarre moves that sometimes work out and sometimes are meaningless... You can learn much more from a human opponent who will help you learn the obvious mistakes by punishing you for them directly.