Given enough free time and the services of an instructor, a character can learn a language or pick up proficiency with a tool.
Preparation. The quality and reputation of your teacher can impact your training. You may optionally prepare for training by engaging in research or carousing to locate a trustworthy, reliable and competent instructor.
Resources. Receiving training in a language or tool typically takes at least five tendays, but this time is reduced by a number of days equal to 5 times your Intelligence modifier (an Intelligence penalty doesn’t increase the time needed). Training costs average 5 gp per day but might be more or less depending on the availability of instructors and the nature of the language or tool proficiency you are training in.
Resolution. For each day that you complete in training, you earn progress towards your proficiency. After training for at least the minimum time required, you gain proficiency in the skill.
Complications. Complications that arise while training typically involve the teacher. Having a shady or low-quality teacher could result in you losing your investment, impact your reputation, or draw you into a conflict.
Player note
Ask your friendly DM for a training tracker card to log your progress for a skill proficiency.