They're breaking down the entire mass into it's constituent atoms, converting those atoms to a form of energy, transmitting that energy to a remote location and reassembling it all
in situ. Somehow, through more-or-less undescribed means, replication is possible, such has happened to Kirk and Riker. Mass can change mid-transport also as happened in "Rascals" [TNG]. It can be possible during lengthier transporter procedures for the person being transported to be aware of his surrounding in the beam as per "Realm of Fear" [TNG]. Certain versions can make this all happen while the person being transported is still moving around too, as per the
Star Trek movies.
--Alex