Training a Proficiency or Language

Downtime Activity: Training PHB p187 You can spend time between adventures learning a new language or training with a set of tools. Your DM might allow additional training options.
  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 of time and money, you learn the new language or gain proficiency with the new tool.
  Source: PHB, page 187

  Downtime Activity: Training XGE p134 Given enough free time and the services of an instructor, a character can learn a language or pick up proficiency with a tool.
  Resources [–] Receiving training in a language or tool typically takes at least ten workweeks, but this time is reduced by a number of workweeks equal to the character's Intelligence modifier (an Intelligence penalty doesn't increase the time needed). Training costs 25 gp per workweek.
  Complications [–] Complications that arise while training typically involve the teacher. Every ten workweeks spent in training brings a 10 percent chance of a complication, examples of which are on the Training Complications table.
  Training Complications
d6 Complication
1 Your instructor disappears, forcing you to spend one workweek finding a new one.*
2 Your teacher instructs you in rare, archaic methods, which draw comments from others.
3 Your teacher is a spy sent to learn your plans.*
4 Your teacher is a wanted criminal.
5 Your teacher is a cruel taskmaster.
6 Your teacher asks for help dealing with a threat.
*Might involve a rival Source: XGE, page 134
 
  https://www.thievesguild.cc/core/downtime/training