The meet and greet is one of the most important parts of the customer service experience. You and your staff will be assessed by your customers within the first few seconds and, rightly or wrongly, they will have formed an opinion about you and your business within that time. Of course, this opinion may change throughout the interaction, but you are miles in front if you do a good job with the meet and greet.
I suggest that every business review its meet and greet process. If someone walks into your business, is it very clear to them what they should do next? Remember that you see the same place, day in and day out, but for many of your customers it's all new.
I find it annoying to go into a business that is ambiguous about what you should do next. Should you go to the counter to place an order? Should you stand around feeling awkward until someone comes and serves you? Or should you start walking around the business until you find someone to help you? It can be very confusing if the business doesn't make this clear.
Motor mechanic garages can often be guilty of this, as are many restaurants. The customer enters the business and then has to stand around until someone comes over to them. In a garage lots of people walk around you, generally trying not to make eye contact. It would take only a few seconds to stop, greet the customer and ask if they need any help. Even if you get asked a few times, it's far better than not being asked at all.
In a restaurant there may be an awkward moment when you are uncertain about whether you should take a seat or wait until someone comes over and escorts you to a table.
Do you have a process for introducing yourself? For some businesses it may be appropriate that you actually shake hands to introduce yourself; for others it may be as simple as welcoming the customer, telling them your name and asking how you can help them.
However it works for your business, make certain that the meet and greet is fast, friendly and confidence-inspiring.