I used to specialize in it when I played in the Army Band. It isn't nearly as dreadfull as it sounds however. When you play in an establishment that isn't specifically geared toward entertainment, you are creating an atmosphere that facilitates conversation and goodwill.
I used to follow one general guideline:
Silence is the most eloquant statement you can possibly make. It will inevitably get everyone's attention, but it will eventually make them uncomfortable as well. Anything you put into that silence should be at least as interesting. If you pace your performance properly, changing up your repatoire with different styles and subtle effects, you will actually gain the attention of your audience, but don't overdo it. If you play songs that people want, or expect to hear every once in awhile, you will gain their appreciation. I used to keep a book with blank pages for customers to write comments on. If I didn't know a particular piece, I would try to learn it in time for their next visit. I would often get more than requests. I would get short endorsements, hints, notes asking when I would be playing there next, (sometimes with phone numbers to call them when I knew) and an occaisional complaint. Complaints are good because you can do something about them. I can try not to play a certain song when a customer is in the room, or we can make sure that they are seated at the other end of the room if they want to have an intimate conversation. If they don't complain, that means you might not see them again and that is always a bad thing.
I kept a list of songs at the back, in case someone wanted to look through and pick something. It doesn't matter what style of music you play, classical, flamencao, jazz, popular, folk, you should have a list of your favorite and smoothest pieces because it always makes you look good when someone requests something you have in hand, and it makes the customer feel like you care about their tastes without having to play name that tune with them.
You need to practice up a few standards for special occasions:
The Anniversary Waltz
Somewhere My Love (Theme From Dr. Zhivago)
Speak Softly Love (theme from the Godfather)
Havah Nagiila (probably spelled wrong)
A few examples. Basically, anything that someone in your area would come up and request to make an event or ceremony more meaningful. These won't be your favorites and hopefully you won't have to do them often, but be ready. You could be the icing on the cake or the fly in the soup depending on whether you can deliver.
Work up several different sets for those times when the crowd isn't interacting with you. You should be able to play at least three to four forty five minute sets, with five minutes to meet and greet customers and a few minutes for yourself (when you gotta go, you gotta go) in between. The reason you want more sets than that however, is that you don't want people saying that you play the same thing all the time. If I am goping to play at the same restaurant for an extended period of time, I might make up as many as five to ten different set lists. I will include one to three songs that I play more frequantly aned interspace them with a variety of songs. You should have a signature tune, one that you don't mind playing whenever called upon to do so, and you want to be sure and aske what your host, hostess or manager likes so they get the benifit of your skills without feeling neglected.
Often a couple or a party will expect to hear a song when they are there. It never hurts to write it down, or ask the host, hostess or manager to cue you. This makes them feel like preferred customers and adds to the restaurant's prestige. If you have already played that song during the evening, try to have a backup, or wait until a majority of the room has shifted (there will generally be more than one seating even in an elegant restaurant) before you play it again.
Most of all, try to enjoy yourself and get into a comfortable space while you are performing. The audience will sense this and your somfort level will reinforce theirs. Good luck and please let me know about your experiances.