Here is a house I wrote that allows for people to train to learn new tools and languages. It is a bit cumbersome, but as a no-combat element that has a large impact, the bulk gives it some substance.
* You may study to learn a new 'extra' weapon proficiency, tool proficiency, skill or language if you 'know' fewer extra (weapon + tool proficiencies + skills + languages) than your Intelligence modifier. You are considered to 'know' an extra weapon proficiency, tool, skill or language if you are proficient, or have any proficiency points (see below) in it. An 'extra' (weapon + tool proficiencies + skills + languages) is one gained through this process rather than from a background, class, race, or magical item.
* If your intelligence modifier is decreased, you lose access to these extra (weapon + tool proficiencies + skills + languages) until it returns to the level at which you learned these abilities (Headband of Intellect caveat).
* At the end of each 40 hours spent in focused study, you may roll an intelligence ability roll (or other ability score roll as specified by the DM as appropriate) with a DC of 15 + your current proficiency points in the proficiency, skill or language (see below), minus your training points in the proficiency, skill or language. If you succeed, you gain a proficiency point in the weapon, tool, skill or language and lose all training points in it. If not, gain a training point in that option (which will serve only to subsequent checks easier).
* Focused study requires training and resources. An expert trainer can give you advantage on your roll. Inadequate resources will give you disadvantage or in the case of a language, prevent you from making a roll at all.
* If your proficiency points equals your proficiency bonus for a weapon, skill or tool, you are fully proficient in the weapon, skill or tool and add it as a proficiency to your sheet. For all purposes you treat i as a proficiency going forward.
* For languages, however, you always need 6 proficiency points to master the laguage. 1 point allows you to read simple messages in the language. 2 allows you to read typical messages in the language. 3 allows you to decipher technical writings in the language. Writing simple, typical and technical messages requires 2, 3, or 4 points. Similarly, understanding spoken requires 3, 4, or 5; and speaking requires 4, 5 or 6.