I have been here about 19 months now and arrived with basically 0 spanish (knew greetings and a cpl of foods and objects). Spent 5 weeks at one of the tourist schools going everyday and since have had a private teacher generally around once a week. I am around it all day at work, seeing as practically all of my colleagues are Argentine. My girlfriend is Argentine.
For the first cpl of months, even with studying I couldnt really have much of conversation and even with the classes, after about 2 months we started switching to Spanish. But it was tough, we would usually just end up in english haha. But, gradually there was less and less english and after 6 months I was conversational and pretty comfortable. Now we both agree speaking english feels odd, I guess the language of the relationship is Spanish. I think I have clearly learnt the most from her, my colleagues and friends and my teacher.
I would not say I am fluent yet (how do you define it anyway), I think to knowing all the phrases and everything, takes years. And although I dont think the pronunciation is so hard, I dont think I am a natural (need to hear a word a good few times before it sticks!!)
Some tips I would give:
1) keep practicing with your partner, listen to her on the phone, with friends and family etc. The key is to train your ear and as you learn the vocab you will understand more and more.
2) getting a really good private teacher. If you can afford it, its so much better use of your time than group classes. I am happy to recommend you mine who is excellent and I have tried a few
3) Interacting with as many locals as you can. And even if they speak english, try and atleast get some time in to practice your english. If not with friends, even with family, friends of your partner etc. Often when I ask what a word means or how you say it, I return that person the word in english and still throw a bit of english in with my local friends and colleagues, so they learn a bit too and dont feel like its all a one way street! Also, lots of praise for them when they correct you
3) listening to the news etc, radio as much as you can. This is difficult at first but gets easier, a lot of them speak clearer and a bit slower.
4) Get a book/source for Argentinian slang. I have a copy of Che Boludo and its a good start, I recommend it.
5) putting up signs everywhere in the house! (really helped with vocab). In fact, I saw the other day at one of my argentines friend house he had magnets on his fridge of like 50 different foods etc. His gf is a kindergarten teacher and had put them up, I think he got them in Palermo at one of the stalls.
All in all, dont put too much pressure on yourself, I know in the first few months I did and I wasnt enjoying it. When I started to relax, everything became much more enjoyable and I seemed to learn faster!