Learning languages

Learning a language is a pretty big deal. It may open up a world of possibilities for a character and their party. As such it should not be taken lightly.
Learning languages from class progression or magic can still be instant and complete. You gain the proficiency and can apply it just like you can with your starting languages.
If you want to learn a language outside the race, class, and background system, you will need to follow a certain procedure.

The system

Progression of language learning is tracked in these 4 aspects:

• Phonology - how words sound
• Syntax - how words are constructed and how they create complex structures
• Semantics - what words and phrases mean but also metaphores and such
• Pragmatics - how we use the language, including its script and cultural aspects of the language

There are 4 tiers of understanding:

• Rudimentary
• Comprehensible
• Proficient
• Native/Scholarly

If you want to be able to apply proficiency with a language you need to have a proficient level of understanding in all 4 aspects. If you fall short in any of these 4 aspects you need to ask the DM if you can apply your proficiency.
For understanding and speaking you will need a tutor or spend time in a community of native speakers. For reading and writing you might get away with just written instructions and a lot of studying.

Reasoning for this system

Whenever we learn a language in school we usually start with studying the vocabulary, which is part of the semantics. We usually do this in written form, which is part of the pragmatics. We start with learning simple words and simple sentences. We can learn this from a dictionary or from a tutor. Later we learn how to communicate with the language. We learn the syntax by studying and the phonology by practising. For a full phonological understanding you need to speak with a native, otherwise we'll end up with Dworcish, the Dwarven-Orcish equivalent of Dunglish.
Whenever we learn a language from interaction we usually start by tying together sounds with their meanings. When one encounters a native speaker the native might point to an object and speak their word for it. One must then learn to match the sound with the meaning. Understanding the sound is the phonology and understanding the meaning is semantics. Especially the phonology develops very quickly and accurately. Soon after the syntax will develop. The cultural aspect of the pragmatics also develops well. The only thing lacking here is the script, which can be confusing when you have a language like French, where you just skip half the written letters when pronouncing a word.
This way of learning can be very powerful and is highly practical. You can be quite sure that learning this way will allow you to put your skills into practice.