In addition to those downtime activities found in the official source books, the following rules are also available for use.
Learning a Feat, Skill, similar relevant Proficiency.
There are official rules regarding learning these on page 231 of the DMG. However they are ill defined and also combine with the later released XGE.
Given enough time and access to an instructor a character may learn a tool or language proficiency.
To learn a language or tool proficiency will typically require 10 workweeks (a Rosharan week being 10 days) minus your intelligence modifier number of workweeks. A negative modifier does not increase the time taken.
In addition to the time taken each workweek will cost 25gp.
To learn a Feat, the same rules apply. However, the time taken is usually increased between 2 to 3 times, depending on the Feat. For each Feat sought, the DM shall clarify the projected time this will take (not accounting for complications).
Downtime activities are intended to take place when a character is between adventures, and subsisting in at least a “comfortable” lifestyle as per the lifestyle rules.
Characters may attempt to learn new abilities when they do not have access to ideal conditions or an instructor. Doing this however increases the cost and time taken to gain a benefit.
For long stretches of uninterrupted travel, totalling weeks or months, a character may continue attempting to learn. The time taken is tripled however due to the other stressors and activities that require their attention in an given day or workweek. The cost is also doubled due to mishaps in learning.
In addition, should a character be attempting to learn something for which they don’t have a proficient instructor then the cost and time is increased. The time taken and cost in materials are both tripled, compared to ideal conditions.
The costs in time and money due to no instructor or ideal conditions stack with one another.
Another player character may act as an instructor for another, however while doing so they would usually not have the time to dedicate to their own studies. Should an player character not be dedicating their entire downtime then their relevant efforts to teach and learn are both doubled.