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.
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.
Given enough free time and the services of an instructor, a character can learn a language or pick up proficiency with a tool.