There are a few topics recently packed with great advice (perhaps search the forums for Jamie D Grant). I also talked about it a little in a recent thread :
http://forums.theory11.com/showthread.php?35509-My-New-Years-Eve-Show-(In-detail!)
As a general rule of thumb, working in restaurants and doing corporate and family gigs, you usually have about 4-7 minutes depending on how many tables you have to hit in the time frame that you are hired for. I wouldn't do more than three effects for a table at a time (unless they are tipping well! At the restaurant, I once got tipped $20 five times from one table. I ended up doing about 40 minutes of magic for them). The reason being is that if you show anyone six tricks, they might remember two and be tired of all the tricks. If you show them three, they will be left wanting more, but feeling satisfied. As well, often, you have interrupted their conversation. So keep it short and sweet.
I have three main sets, each with three effects, and a fourth set with two effects. I have done some gigs, where I use one set all night long because the tables are well spaced, however, most of the time two sets will work perfectly. At my last gig, I spent some extra time at one table and did all four sets over the course of the night.
Simply put (and Jamie says this too in his post), nine effects will be great. Make sure you perform them all well, and your patter is solid (your patter will also develop and change as you perform for real people and hear/see reactions to the lines you speak). Remember the goal is to be entertaining, not just have an impossible illusion.
As to your question, about approaching tables, this isn't easy. Eric Mead in his book talks about his approach, and he says it's like you need to sell your show to a new group of people over and over through the night. As soon as you finish one performance, you must find a new audience, and convince them that your show is worth watching. Eric's approach is brilliant.
For me, I am often working with adults, and I usually say something to the effect of "Good evening, sorry to interrupt your conversation briefly. Are you enjoying your night so far?" (they respond-usually good) "Fantastic. Hopefully I can make it even better. My name is Justin Morris, and I am the magician this evening, and I was wondering if I could show you a little of what I do." (Wait for a response) "Wonderful" (begin routine)
Some people have different approaches. Professional magician David Stone wrote in his book that he approaches tables and begins the magic before they even know that he is the magician. This is 180 degrees different than Eric Mead's approach. Both work for them.
Some would disagree with my approach and say that if you ask them if they would like to see some magic, they might say no, thinking that you are a cheesy children's magician. Although I have had this happen twice in the last ten years, I feel that asking them gives them some control and sense of dignity. I would most certainly prefer to be approached that way than accosted with a flaming wallet. And perhaps that is the question to ask yourself. If you were out with a group of friends for drinks, or a nice dinner with your girlfriend/wife, or out for dinner with your kids and things are a bit chaotic getting everyone settled, - how would you like to be approached? Would you prefer someone reaching into your ear and producing a sponge ball? Or would you rather someone strike up a conversation first and get to the magic in a bit, or somewhere in the middle? All approached can work depending on your style. But if you believe in the approach, it will just come natural to you.