5E has a built-in system for dealing with activities that the characters focus on between adventurers. While I agree with much of it, here are a few tweaks that I prefer (and will use as House Rules). This may be updated with more details, as there are a large number of downtime activities in the PHB, DMG and Xanathars guide.
Learning Languages or Tool Proficiencies
- Normally this would take 250 days of effort, with a cost of 1GP per day (this is aside from your normal cost of living). – PHB pg 187
- My take is that it is 120 days of effort (assuming a full day of focused work and suitable location), with a cost of 1GP per day, or half that cost if the instructor is another PC.
- Looking to do it faster?
- In the case of languages, if your instructor natively speaks the language and you are immersed in that culture (EG: Learning Elven from an Elf while living in an elven city, or Dwarven from a Dwarf while living in a Dwarven Fortress) without break the total number of days of effort is only 90.
- In the case of Tool Proficiencies, if you immerse yourself in that trade (such as working in a Brewery every day for months without more than a one day break), you likewise reduce the total number of days of effort to 90.