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This is the most important part of keeping a conversation going with anyone, from your girlfriend, to you grandfather, to the kid next door. People like to talk about themselves as a general rule, and if you open that conversational door, most will walk through it. Try to ask more open-ended questions, and avoid ones with yes or no answer. The idea is to ask things that will lead naturally into conversation, not to pepper her with interview questions.  Ask about her day. This is an obvious place to start. When asked simply, “How was your day?” many of us automatically respond, “Fine thanks,” without even thinking about it. This probably won’t lead anywhere. Instead, try something a little more pointed, like, “Did you do anything interesting today?” or “Did you make it to work before that storm started this morning?” It may not lead to anything particularly fascinating, but it will ease you both into the conversation. Ask about mutual interests and acquaintances. More than likely, you and your girlfriend share various interests. This is a great way to introduce a subject you can both talk about, while still framing it as a question. Try asking what she thought of latest episode of a TV show you both like, or if she read a recent interview with a mutual favorite author, or if she’s seen so-and-so lately. Ask for support or advice. It is important to offer your girlfriend a sympathetic ear and a shoulder to cry on when she needs it, but if she feels like you never need support from her in return, she may begin to feel like a burden. No one wants to date an emotionless robot who never needs help. Don’t invent problems if none exist, but if you are struggling with something, don’t be afraid to get vulnerable and turn to her for advice or validation. Ask what she wanted to be when she grew up when she was 7. This is a bit of an unusual question. It will show her that you are interested in learning more about her, and give you some new perspective. If something particularly funny or interesting happened to you today, tell her about it. It can be easy to rely too heavily on gripes about frustrating situations when you do this, so try to make sure you are not just rattling off complaints. Brainstorm fun things the two of you could do together this week. If you already have plans, talk about how excited you are to go to that concert, or mention a review you read of the play you are going to see. This will help her get excited too, and make her feel like a valued part of your life. You don't want to monopolize the conversation, but no one likes to date a person with no ambitions. Tell her about some of your hopes and dreams. This should constitute a small portion of your conversation, and you should avoid anything too brutal or personal, but this can be an easy fallback if you are at a loss. There aren't a lot of people who can resist indulging in gossip from time to time. Inviting her to tell you more about something she just said will let her know you are interested. It will also extend the mileage you get out of that particular subject, saving you from immediately having to come up with a new topic.
Ask lots of open-ended questions. Share an anecdote from your day. Make or discuss plans. Share your goals and aspirations. Gossip. Follow up.