Undoubtedly, the backbone of any language is grammar. So when learning a new language, is it essential that you learn grammar and internalize it. However, many people differ in their opinion of how to go about this. Some people like to fully understand grammar before really using it. Other people like to learn naturally through conversation and context. Both have advantages and disadvantages. Try them both out for yourself and see which one works best for you. The Korean learning journey is not so much a set path as it is one of experimentation. Try things, see how they feel, adapt. Rinse. Repeat.
Korean University's Free Online Korean Courses - For those who want to take a class but don't want to fork over the cash right away, this is a really good resource! You can register for the class if you like (although this seems to be difficult for some people), or you can just go through the videos on their Youtube channel here! As you go through the videos, take notes and if you have questions, you can ask your coach!
Go Billy Korean - Excellent resource for learning grammar. These videos explain each grammar point in depth and include realistic examples too. There are also videos that teach you useful expressions to use in Korean conversation.
How to Study Korean - Good explanations and helpful grammar points. Provides vocabulary for each lesson but little explanation of the vocabulary.
Talk to Me in Korean - Probably the best all around resource for learning Korean. They've got a little bit of everything! But their structure can be hard to follow sometimes. Give them a try and see for yourself!