First, you must find an instructor willing to teach you. The DM determines how long it takes, and whether one or more ability checks are required. The training lasts for 250 days and costs 1 gp per day. After you spend the requisite amount o f time and money, you learn the new language or gain proficiency with the new tool. – PHB Part 2 Adventuring p.187

I have been reading for the last few days. 5E has made and effort to be as vague as possible. So I will point out some important details.

There is no half skill in D&D 5e. You are good at it or you roll a stat bonus. The logic is you are skilled or unskilled. Nothing else. Some games treat Skills and Languages as a % but D&D has nothing like that. By game mechanics you are Fluent or nothing else. I have room to roll your effort with a difficulty rating to see if you make your point.

The D&D devs dealt this should only be done during down time. We will ignore that rule.

Home Brew Languages

I want to try and keep this fluid but at the same time I don’t want to give things away.

Points:

  • To learn a new language is 250 days.
  • MUST have an instructor with (at least) 13 in INT and WIS.
  • You must spend 1 hour a day learning. More time does not matter.
  • When you learn a language you learn to speak it and read it. Yes, orcish and goblin have written languages.
  • Each day will cost 1gp, to express the expense for paper, ink and other things. Supplies must be written on character sheets. No supplies means no learning. 
  • Some languages may take longer, while others may take less time. For example, if you know Elvish or Sylvan, I would let you take half as long to learn a language. Some languages are their own and have no root or are the root of another. Exotic languages (Draconic and Celestial) are unique languages and will take the full 250 days (minus INT bonus x 10).

Exceptions and Advantages:

  • Characters with a high INT can use that to their advantage. 250 days – (INT Bonus x 10) = the number of days less it takes to learn a language. And INT bonus of 3 means 30 days less on the 250, so 220 days instead.
  • Every 25 days I will roll a DC 13 challenge. You roll D20 + INT bonus and if you roll 14 or better I do not add days to the training.
  • Every Fail I will add 1D4 days to the training process.
  • Critical success (Nat20) I will roll 1D6 and subtract from your training days.
  • Critical failure (Nat1) I will roll 1D4 and add to your training days.
  • Elvish and Sylvan are related and learning one or the other is 100 days less.
  • Dwarvish, Gnomish and Halfling related and learning one or the other is 100 days less.
  • Orc and Goblin are related and learning one or the other is 100 days less.
  • If you fail the last roll, I will roll 1D10, that number will be how many days before you can roll again.
  • A break of learning, starting at 30 day, will incur a difficulty on the following rolls. Critical success and failures will help or hinder this process. I will review this on individual bases.