In ACM Ubiquity, there is a nice article Philip Yaffe: Fast-tracking Foreign Languages: How to Meet the Linguistic Challenges of Working Abroad about learning of foreign languages.
It is somewhat directed at english-speaking people who might tend to believe that it is near-impossible to learn other languages ... but points out that many people do, actually quite seamlessly - especially if one is concerned mostly with speaking (at least first): the redundancy of language lets other people understand even quite malformed sentences. And, contrary to at least some schools, grammar is the least important - the big effort is the vocabulary (which is, after the base vocabulary, best done through reading).
He thinks that one mostly needs to change one's mindset - from perfect speaking to perfectly communicating.
I therefore suggest that the most effective order for learning a language would be:
1. Basic grammar
The minimum necessary to put together an intelligible (if incorrect) sentence. In my experience, this is most efficiently done self-taught. Sit down with a grammar book for about 10-15 minutes each day until you begin to feel somewhat comfortable with it.
2. Basic vocabulary
The minimum necessary to begin using the basic grammar. Again, in my experience this is most efficiently done self-taught, i.e. the classic "learn five new words each day". It won't be very long before you start seeing how different words are related, so you can begin to guess what new words mean without resorting to the dictionary.
Speaking the language
Putting basic grammar and vocabulary to work as soon as you can actually begin using them. This is the time to consider a language school or a personal tutor. With the foundation of what you will have already learned by yourself, you will certainly progress more easily and rapidly than if you had leapt into formal language instruction at the very beginning.
Writing the language
You will almost certainly never need to do much writing. And what you do write will certainly need to be revised and corrected by a native speaker.
Since vocabulary is crucial, then the largely unrecognised key to mastering another language is: Learn to read it.