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.
I wouldn't say convert atoms to a form of energy, since you would probably lose what made up the original atom if you changed it, it's more like you get ripped apart like atom sized Lego Blocks and get reassmbled.
As far as changes happening while mid transport, every incident was due to outside interference. The transporter itself didn't do anything to cause said changes. Starfleet still doesn't have a good idea as to what happened since those were one time events and not repeatable for testing.