[draw] on (a|the) (cigarette|cigar|pipe)

to inhale smoke from a cigarette or another object that produces smoke

Despite the health risks, he continued to draw on his cigarette while deep in thought.
The old man sat on the porch, quietly drawing on his pipe as he reminisced about the past.
She looked out the window, absentmindedly drawing on her cigarette.
The group of friends gathered around the campfire, chatting and drawing on their cigars.
Trying to ease stress, he took a break to draw on his electronic cigarette.