To take small sips of a drink over a period of time. My favorite thing to do is watch the sun come up while I sip at my first coffee of the day.It always makes me self-conscious when someone I'm out with sips at one or two drink throughout the whole evening while I'm getting a fresh pint every half hour.
sip at
or sip on
v.
To drink from some beverage in small amounts at a time: The skier sipped at the hot coffee at the lodge. She was sipping on a cocktail at the bar.