Charisma points are primarily gained by talking to oneself in the mirror. In The Sims 3, Charisma can also be gained by talking and interacting with other Sims, as well as reading Charisma skill books.
In The Sims 3, certain interactions and rewards increase starting relationships, such as a Celebrity using a Charming Introduction will instantly have a new friend. Charisma skill-building requires friends and relationships to progress. Charismatic Sims learn the skill faster.
In The Sims 4, Charisma is only one of the social skills, and is used to advance in Friendly and Normal social interactions (Comedy focuses on Funny interactions, while Mischief on the interactions of the same name).
Sims who are teens or older can use a mirror or medicine cabinet to increase their Charisma by choosing "Practice Speech" or "Practice Romance."[TS2][TS3]Sims with the Good trait have the option to Practice Speech For World Peace, and those with the Evil trait for can Practice Speech For World Domination.[TS3]
Teens through Elders can practice being the 'Most Charismatic of them all" at the magic mirror![TS3SN]
Text: A local politician that's been keeping an eye on you thinks you should put in the effort to improve your Charisma skill. To make this worth your effort, you'll be paid to improve your Charisma skill by just one level. Seems like a good deal!
Smooth, Like Verbal Butter
Received: Reach Level 5
Goal: Use "Smooth Recovery"
Text: Sims like you tend to get into a lot of conversations. Unfortunately, not every comment will land favorably upon the ears of its recipient, so you'll need to learn how to get out of sticky situations. Use Smooth Recovery to fix a social faux pas and you'll earn a little cash for your efforts.
A Charming Experiment
Goal: Assist Experiment at the Science Lab
Text: The Science Facility is conducting experiments to see if charming Sims can convince creatures to do things they don't necessarily want to do. This week, the scientists are paying cash to any Sim that can convince ants do dig holes in specific areas. Travel to the facility to show just how charming you really are.