The next time you talk to someone before you open your mouth to speak think about this person more closely. What may you not know about them? Ask that! You'll end up with a richer conversation where you get to hear something new.
Step 2: Master Open-Ended Questions
Remember when you were a kid and your parents asked you "how was school today?" and you replied "good". That question was actually your parents way of trying to get you to talk except you foiled their plans with your one word answer.
Instead of going the simple question route why not try an open-ended question. This is a great technique to use if you're speaking with someone very shy or introverted. It forces them to not only give a longer answer but to potentially share something unique about themselves they never thought of sharing.
Sit back, relax, drink some coffee and listen to what the person has to say. The hardest part of this is not waiting for them to stop talking just to tell your story. Instead simply listen.