Short Answer: I tried to talk to people everyday and took lots of notes. It took 3 years before I was reasonably fluent and started teaching the language to other foreigners.

Long Answer: Here's how I learned to speak Thai as my 2nd language.

I moved to Thailand in 2003. I had very little experience with any type of successful language learning. I had 2 years of high school Spanish which means I could ask where the bathroom is and knew the difference between "dog" and "but."
I didn't know any Thai when I got on the plane to fly there. I bought a phrasebook the day I left and tried to learn the numbers and a few basic phrases on the flight.

I improved a tiny bit each day. Every day people told me how great my Thai was. It's a nice motivator for a while. I made some half-hearted attempts to learn the script, but I never really understood how the tone system worked nor did I have any clue that there were multiple ways to say a P sound and that this was actually crucial to being able to speak well.
After 1 month, I did a visa run to Laos where I used my "awesome" Thai to help some other travellers haggle prices and kept us from getting ripped off and also just helped connect with regular people who couldn't speak English.

The next major event was a couple of months later when I got a job and ended up moving to another city halfway between Bangkok and Chiang Mai. I left Chiang Mai thinking I was pretty fluent in Thai, but I quickly discovered I was very wrong. In the new city, I struggled to understand what anybody was saying and I was having to repeat myself all the time wondering what was wrong with everybody. I eventually accepted the fact that it was me rather than everyone else which was the problem. I also had no idea how to fix it. The people I worked with tried to be helpful, but they couldn’t really explain what I was doing wrong.

At the end of the year, I moved back to Chiang Mai and started studying at an university there in order to get a visa and take some Japanese classes. While studying at a Thai friend’s house for final exams, I noticed a large black book about Thai language that I had never seen or heard of before. I believe it was written in the 50s for ambassadors and other foreigners who were in Thailand and included things like how to talk to their servants as well as sample writings from both educated and uneducated people. I photocopied the book and went through it over the coming weeks. The book broke down the entire sound script, sound system and tone rules. It wasn’t well laid out and I could write a mile long list of things I didn’t like about it, but it was the first comprehensive explanation I had come across.

I spent about 6 weeks studying and drilling all the exercises and eventually remapped them so they were more useful. I have almost no attention span so I would do very short study sessions a few times a day. A session wouldn’t usually last more than 5 minutes and might be as short as 1-2 minutes.
I remember the day when everything clicked. Words that I used to mix up because I thought they sounded similar were suddenly so clearly different that I couldn’t believe I had ever mixed them up in the first place. I knew the tone system so well that when I pronounced something with the wrong tone, alarm bells would go off in my head “That can’t be a low tone because it’s spelled with a low class consonant!” and I would instantly self-correct.

This all happened very fast and my fluency level just skyrocketed at this point because once I learned how to say things correctly, it became easy to hear them when others spoke. I still wasn’t fluent, I still made mistakes, but I gradually fixed any pronunciation mistakes I had been making.
Every single effort I made to learn Thai up until that point was always severely hindered by the fact that I did not have a solid grasp of the sound system.

Once I was comfortable with the script, if I encountered a new word, I could just jot it down in a little notepad I always carried and I could look it up later. Even if I didn’t know exactly how to spell something, I could at least write it out phonetically and then ask people what the correct spelling was. If I tried to say something and I got a weird reaction, I’d write down what I said and ask 4-5 of Thai speakers (never ask just 1!) how I should have said it. That meant that next time it came up, even if I had forgotten the new sentence, I could look it up because it was in my pocket. I’d fill up one of those notebooks every month or 2 and I believe I retained about half of whatever went inside them.

I believe that there are a few key steps that you can follow to make significant progress in the first 1-3 months of learning a language:
Getting Started with a New Language:

Step 1) Learn the sound system

Actually spend a few days learning how to say the sounds properly. How much time will depend on the language This can go a lot faster if you find someone who can explain things like where exactly your tongue is supposed to be to say a particular sound. Non-native speakers who speak a language really well tend to be more helpful than native speakers for this.

Step 2)Learn short, high-frequency sentences and/or dialogues

Make or find a list of sentences/dialoges and learn to say them correctly and as you get more comfortable. Start slow and practice saying them faster until you can call them up automatically. When you have 20 or 25 of the right sentences, you will then have enough ammunition to start faking a conversation.

Step 3) Talk to people as often as possible
Even if you have just 2 or 3 sentences, you can already go out there and blast them off at people and see where it leads. It’s fun and the stuff you learn putting these into practice is far more likely to stick because it happened in a real life with another human. You may need to hear some things 10 or 20 times before you really get it and that’s perfectly normal. If you are paying attention and keep hearing something over and over, you’ll remember it eventually. Some stuff will slip in even when you aren’t paying attention. If you aren’t in the country, practice on your pets or your friends, but since it's 2016 and you can fly across the world for under $1000, there's really no excuse to not go there. If you really can't go, then use sites like italki.com and hire private tutors. If you don't have money, do language exchanges.

Avoid word lists in the beginning.
Knowing how to say “Are you going?” quickly and with good rhythm and pronunciation has far more value to a beginner than “purple, aunt, cloudy, bird” or “ shoes.” Once you have structure and sounds, taking on new words is much easier.
I focus on drilling sentence patterns rather than memorizing grammar rules.

Ideal sentences/dialogues will look like this:
The shorter and more colloquial, the better. E.g.,
A: What'd you do yesterday?
B: I saw a movie.
A: How was it?
B: Not bad.

It’s generally ok to take some of those initial sentences from courses like Teach Yourself and Assimil if that’s all you have available, but I’d definitely put off learning anything you can’t imagine yourself saying today or tomorrow. I created a list of sentences for my students a number of years ago which you may find useful. Feel free to copy and modify. https://docs.google.com/spreadsheets/d/19OQdDLq9MBoGpPy9I7rB....

It’s worth noting that while in Thailand I took years of classes each in Chinese, Japanese and Korean. While I eventually learned to speak all 3 of them as well, I have never reached a level of fluency anywhere close to what I did with Thai. I even 2 spent solid years totally immersed myself in Japanese (using AJATT mentioned below). I had headphones in my ears blasting Japanese whenever I wasn’t talking to someone. I watched The Matrix, Shawshank Redemption and more dubbed in Japanese hundreds of times. I'd rip the audio, shuffle the scenes and listen to them when I slept, walked or exercised. I read piles of manga and novels translated from English. It turned out that none of that was a substitute for actually talking to people everyday like what I did with Thai. You need to be trying to talk to as many people as possible for an extended period of time in order to achieve any real semblance of fluency.

3 years after arriving in Thailand I started to teach Thai to a couple of friends. It worked great, and over the course of teaching a couple hundred people, I developed and tweaked a new more efficient approach to learning Thai. This is only important here because this is how I ended up teaching Thai and it worked so well that it changed the way I learned as well. Less steps, more sentences, no memorizing word lists.
And for the sake of credibility, here’s a video of me speaking Thai in 2009, nearly 6 years after I got to Thailand. I was pretty camera shy, but it’s a general idea of what I was capable of at the time. https://www.youtube.com/watch?v=mgzXuHmO_HY