Reaching a conversational level initially looks like learning a language normally, so it will be good to familiarise yourself with the main ideas. Any good language learning advice will tell you to emphasise using comprehensible input (texts and audio) as much as possible, and this is something you should do. Where this technique differs is, firstly, what you don’t do, and secondly, how early and aggressively you practice listening and speaking. The speed aspect of the technique is achieved by cutting non-essential aspects of language learning.
First, cut out advanced grammar. You can do a lot with the simple stuff.
The same goes with words. Ignore the rare, long, and complex words. Focus on those word that are most useful and easily learnable. You only really need the most common thousand words to make yourself understood in a basic conversation. You can refine your list further by specifically learning the kinds of words involved in conversations people might have with you. These tend to be words that cover reasons for learning, goals, inspiration, interests, and your opinions about the language.
Finally, focus on learning some natural-sounding phrases. This is an important tip for all language learners. Pre-learned phrases can be very helpful and make you sound more fluent. For example, many common phrases and filler-words (such as “it’s like”, “after that”, “in short”, “and so”, and even just “umm”) can sound quite different in other languages and not use vocabulary that directly translates to the English equivalent. Learning these is important and will make you sound much more natural.
Now on to skills. Focus less on reading and writing in favour of speaking and listening. You will need to focus very strongly on getting lots of speaking practice through conversation. In addition, you will need to get good at listening, so focus on that, too. A core principle of learning is to consciously practice the thing you want to be good at. You want to be able to speak, to get better you need to practice speaking. Listening is also a difficult aspect many learners leave till later due to its difficulty. You won’t have that luxury.
Next, learn good pronunciation. It will go a long way towards helping you sound fluent, even if you flounder in a lot of other areas. Good pronunciation generally takes a lot of practice. Many guides and resources will discuss it, you need to focus on it.
One trick, which you should not use if your goal is to improve rather than show off, is to direct the flow of conversation. When talking with someone you can push the conversation towards familiar topics. This will help ensure you have a successful conversation.
Your goal should be to be able to speak at a close to natural pace without too many unnatural pauses, occasionally busting out some pre-learned filler words/phrases when you get stuck.
With a lot of work you can do this in about 4-12 months, depending on the language. In five years you could theoretically impress all your friends with a good basic level in 8-10 languages.
If you’re learning for travelling, then much of the same ideas apply. In addition to the top 1000 you can learn travel phrases and words related to your experience in the country.
It’s also worth noting that it’s entirely possible to learn using the internet as a sole resource. It will be more difficult for people who struggle to find motivation and can be slower depending on how much time you put in, but it allows you choose your own style, pace and curriculum.