Though it's a common phrase at virtually every dine-in eating establishment, it is important to welcome your patrons to the restaurant as a way of greeting the table. How you welcome them is largely dictated by the class of the restaurant. If it's a family eatery, you might simply say, "Welcome to Bob's Diner." If it's a classier establishment, your supervisor may have given you a precise welcome greeting to share with each table's occupants.
Many waiters say their name to their patrons as a form of greeting. Often, the statement will sound something such as, "My name is Dave, and I'll be looking after your table tonight. If you have any questions or concerns, don't hesitate to ask for my by name." With this type of greeting, you're connecting with your patrons on a personal level and letting them know your name. Doing so, however, has a second purpose. If you provide exceptional service, your guests already know your name should they choose to recognize you to a restaurant manager.
After you've offered the initial welcome and introduction, you may inform the guests of the restaurant's specials as you present the menus. Typically, a restaurant's specials aren't included on the menu, so it's important to convey this information as part of your greeting to the table. If the guests are still getting settled when you first arrive, you may wish to outline the specials at your next visit to the table.
As a waitress, your key task is to deliver the food on time, effectively and with a pleasant demeanor. It's also important to give as much information about the restaurant as possible. For example, you may choose to offer some basic advice -- where the washrooms are located and where the coat check is found -- after your initial introduction. If the restaurant has a unique aspect, ask your guests if they've previously dined at the establishment. If not, explain the unique side of the restaurant. You'll be seen as helpful and may be rewarded when the guests leave their tip.