Dancing to the level of partner
It often happens that the two partners dancing socially are not at the same level. It is important that the more experienced partner dances at the level of the less experienced partner. This is mostly a comment for leaders: when dancing with a new partner, start with simple figures, and gradually work your way up to more complicated patterns. You will discover a comfort level, file it away in memory for the next time you dance with the same partner.
The same principle applies to Swing followers, although to a lesser degree. Doing extra syncopations, footwork, free spins etc. can be distracting and even intimidating for a less experienced leader. More often, because of the information passed by the hand connection, a new lead may misinterpret the fancy footwork of the follow as a mistake on his part (it takes a while before new leads can distinguish the information received through the hand connection as not coming from their own body).
Be personable and smile. Try to project a warm and positive image on the dance floor, even if that is not your personal style. Once one asks or accepts a dance, it is important to be outwardly positive, even if not feeling exactly enthusiastic.
Maintain eye contact - you are dancing with this person, therfore it is respectful to pay attention to them. Do not let your gaze wander to things or people around you.