I taught myself to do this. I was not exactly shy as a young person, but I was very reserved and tended to be socially passive, allowing others to come to me rather than extending myself. I decided to change the day I realized that this meant I never got to choose my friends but only to have the friends who chose me.
The method that worked for me was to deliberately forget about myself and my own interactions and make myself responsible for facilitating others’: being hospitable, introducing people to one another, helping others start conversations, making others feel welcome and at ease. This was difficult for me because I was not taught much in the way of social skills—my father was an ivory-tower academic, and my mother, though more gregarious, was relatively socially inept and naive. My school friends were the “smart” kids and not the “popular” kids, and we got on well together but without having any special knack for it. I learned a lot by observing the reactions of others and by watching those who did this well. And I found that people tended to treat me more in accord with my friendly intentions than with how good I actually was at it. With practice I got much better. I remained self-conscious, but I did not let self-consciousness govern my behavior.
In time people came to perceive me as more outgoing than I actually am. I can strike up a conversation with a stranger and take it to someplace interesting, even sometimes fairly deep, within a few minutes’ time. I can smile and greet people and remember names. I can take care of guests and remember all the details and see to everyone’s comfort. I can survive long parties without languishing in a corner.
It costs me plenty. I am still one of those who answer that one question on the personality inventories by saying that social interactions do not recharge my batteries but deplete them. But I generally find them to be worth the effort as long as I don’t have to do it more than once every few weeks.
When someone’s behavior changes for the better, I usually see that an effort is being made and try to support it. If I noticed your new manner, I might comment by saying “I see that you seem to be enjoying social events more these days.” Then if you wanted to talk about it I would encourage what you were trying to do.