There's really not much to dining out alone. Firstly, you have to realize that not everyone is staring at you when you walk in by yourself. Generally, others are absorbed in their food or gabbing away with someone, and they don't even notice you. They may glance up, but generally no one stares or makes rude comments.
Some people like to make use of all the time they have and get some work done while they dine.
I personally do not. This is the 90's, and if you are a woman, dining out alone has long since been an anomally. Sometimes you might get a host or hostess who may look confused, but that's their problem, not yours. For me, dining out almost pars with a kind of meditation. I change my seat if I can so my back will be facing him.