21 years as a sale person, sales manager and sales trainer...
Your first job in this meeting is to find out what they need... Ask a question, then shut up and listen to their answer... Biggest mistakes most people make are talking too much and not listening enough.
If you ask the right questions and listen carefully to their answers, they will tell you what they need, help you prioritize it, and give you lots of clues what they are willing to pay...
Once the fact finding is done, if you are ready with the answers you get to do a short presentation of what you can and will do for them, how much it will cost, etc. Be sure to ask more questions along the way, such as "Is that what you were looking for?", "That's what you wanted, isn't it?" "How does that sound?". At the end of your presentation, ask them if there is anything else they were concerned about. If there is, address it right away. If not...
Then ask them to buy, such as "Okay, I think we've covered everything. Shall we get the paperwork done now and lock in the date in my calendar with your deposit?" shut up and wait for their answer. This is another time many people screw up and just can't keep their mouths shut. Don't say a word. Let them answer. If they have any reservations, they will let you know and you might have to go back and address that concern, then re-ask them to buy.
It takes as long as it takes. Don't rush it. Just try to relax. Watch their body language. Emulate it and try to control it with your own body language. Sit back to relax, lean forward for emphasis. If they cross their arms, they are not believing something you said. Try crossing yours too, then uncross yours and sit back.... see if they do the same.
But don't put too much thought into it.... Just try to be yourself and treat them as you would want to be treated, if you were in their shoes.
I don't shoot a lot of weddings, but when I do I take a "shot list" menu along, that lists about 150 different specific shots. It's a great organizing tool and helps flush out all the details of what the client will want done.
I prefer to meet with them on their own ground... in their home, office or anther meeting place of their choice. They will feel more relaxed and comfortable there. Their home or office can give you a lot of clues about them. If there are lots of photos around, they will likely be good customers for prints or a photo album, for example. If the photos are of them and lots of different friends or family, they might be really good for some references.
If they prefer to meet in some more public place, no problem. But let them pick the location. That way they can't pull a no show or be an hour late and say "We got lost trying to find it."
Don't force it. If they are reluctant to commit, find out why. It might be as simple as they have a list of three photographers they are interviewing and you're the first one. In that case, find out when they are meeting with the other two and ask their permission to call them the day after they talk to the last one. Don't leave it up to them to call you. Ask what day and time to call them, then do so on at that time.
Also use your sixth sense during the meeting about whether it will be a "good fit". If you are uncomfortable with them and/or they are uncomfortable with you, the job could turn into a nightmare and might not be worth pursuing too strongly. Of course, it sort of depends upon how badly you need the job!