The simplest answer as to character introduction is presenting the character in some sorta situation that shows who they are, like key points from a day in work, a chat with a friend, an escape from somewhere. This sort of stuff.
One thing I find both important and helpful (but often fail to do in practice) is to describe only what's important for the character and situation. For example, don't go describing the main character's appearance, personality, neighborhood, world or anything just out of the blue, but go slightly off tangent to make some key points when you have a reason to. It really ruins the mood when you describe character's appearance in the middle of a fight or escape or something. You should focus on actions and emotions here, and you will have the introduction of the personality. Wait till it ends and the character is treating wounds, and put some info about the appearance alongside their actions.
As for subtle worldbuilding, I'd just put some key information in dialogues or character's thoughts.