puff (away) at something
1. to blow at or into something in puffs. She puffed away at the beach ball, blowing it up as fast as she could. Todd puffed at the fire until it grew larger.
2. and puff (away) on something to smoke something, such as a cigar, cigarette, or pipe. Scott was puffing away at his pipe. She is always puffing on a cigarette.