There are hundreds of ways for magicians to approach a new group of people, and each magician needs to find ways that work best for them. Having a successful method of approach is good, but having one that increases the applause you will get, is even better.
I've been using a particular introduction for groups and especially for mid size tables (6+ people) for around 8 years now. It's called The Accidental Volunteer.
The Accidental Volunteer Introduction.
As I walk up to a new table, I look for a person that I feel would be a good assistant for my first trick. This could be someone that was responsive during the pre-dinner strolling magic period. It may also be one of the people to the immediate left or right of a dominant alpha spectator. Picking a responsive person is not because of the introduction I'm about to say, it's because I'm about to turn that person into an accidental volunteer.
Here's what I say:
To the spectator:
"Excuse me, what's your first name, please? (Wait for answer i.e. Kate) Ah, yes it is Kate isn't it!"
To the whole table with a massive cheeky smile:
"Ladies and gentlemen, please give Kate here, a BIG round of applause for volunteering!"
To the spectator:
"Thanks Kate, that's really nice of you!"
(Quietly to her:) "Don't worry Kate, this will be fun."
I then perform my opening trick and my new assistant will help me. The opener magic trick may differ, but there is usually some way to build in a role for the 'assistant' to help.
Why this works so well
This introduction is designed to do the following:
1) It engages the whole group at once together.
2) It politely stops any member of the group from not paying attention, as they have a social activity of applause, for a fellow guest to make them engaged.
3) It produces a laugh and creates a sense of fun right from the start.
4) It primes a spectator to work with you.
5) It points out to the group that applause is an acceptable and expected reaction to close-up magic.
6) It doubles the amount of applause the whole room hears as spectators clap at the beginning and end of the set.
7) It relaxes your helper/spectator as they see you will get the group to appreciate them.
8) The Alpha Spectator will be one of the most enthusiastic clappers as it's their 'table partner' involved.
9) It raises anticipation from other tables about what is being shown, so you get other tables calling you over as you walk around choosing your next table.
10) The other spectators will give a whopping round of applause to the spectator, partly as they are showing support to him or her and partly in relief at not being picked themselves. It also gets laughs as the other guests enjoy the situation of an accidental volunteer.
This approach may or may not work for you. Your persona may be decidedly different from mine. Try it out sometime and see what happens. I love what it has done for me over the years, and I think you will genuinely like the results.
Image courtesy of 42andpointless