At this point, there are two options. The ruthless strategy involves cynical manipulation of people for your ends, "games playing". The responsible strategy means caring, giving attention to people's needs, and acting like a human being. This second option, while riskier, is more appropriate for the shy person, and indeed for any moral person.
Ruthless Strategy:
Single out the "important" people, and ignore the rest. Approach, in
succession, each group of persons you wish to influence. Adopt a facade
of aloofness (slightly understated arrogance), detachment, and a lack of
involvement - a guise that projects personal power. Aggressively push
"hot buttons" to manipulate the person you are facing, then briskly move
on to the next. Spend time only with those who can serve your purposes.
Leave envy and emotional wreckage behind you (what do you care?).
Responsible Strategy:
Seek out the "loners", the people like yourself, the ones who appear
shy, lonely, in need of attention. Give the necessary emotional support
to everyone you speak with. Listen attentively. Be open and sympathetic.
Take the time to satisfy other people's needs. Respect others' feelings,
but be prepared to have your own hurt. Keep your presence of mind and be
resilient. Leave joy and healing behind you (you care).
"Working a room" is a variant of the art of mingling, of blending into
any given space containing groups of socializing people, of becoming part
of the 'action'. Making the transition from foreground to background,
from intruder to "one of us" is no easy matter, and requires
considerable finesse.