Praise be to Allah.
Improving one’s level of social intelligence requires intellectual effort and acquisition of knowledge, as well as practical, behavioural effort.
With regard to intellectual effort and acquiring knowledge, it is attained by learning the noble characteristics that have to do with dealing with people in general terms, and learning the ideal ways of dealing with transgression and hypocrisy, and bad characteristics in particular.
With regard to practical, behavioural effort, it is attained by persisting and steadfastly interacting with people on the basis of noble characteristics; developing self-restraint when dealing with transgressors, hypocrites and ill-mannered people; and repelling with that which is better and bearing with patience the evil of wrongdoers.
The best and noblest path that one may follow in terms of both knowledge and behaviour in this regard is the teachings of the Prophet (blessings and peace of Allah be upon him) on how to deal with people of all types, ages, religions, races, classes and statuses.
A useful book that we advise you to read in this regard is the book Kayfa ‘Aamaluhum by Shaykh Muhammad Saalih al-Munajjid, which clearly explains the teachings of the Prophet (blessings and peace of Allah be upon him) regarding how to interact with people of different types.
See also the answer to question no. 71184, which speaks concisely about the character of the Prophet (blessings and peace of Allah be upon him).
And Allah is the source of help.