There are any number of books, pamphlets and on-line sources which document and explain the Orthodox practice of fasting during lent and other seasons and days of fasting. You can look these up. Basically, some days are more relaxed than others, but the fundamental concept upon which the various relaxations and exceptions are built is abstinence from animal products (meat, fish,dairy) as well as from wine (alcoholic drinks) and oil. This means that the basic lenten diet is a vegan diet as well as oil-free and alcohol-free.
So the big picture or the big principle is the recommendation that, subject to health considerations for a very few, Orthodox Christians should attempt to follow a vegan diet during fasting seasons and on fasting days. Of course, when we say a vegan diet we are also talking about avoiding expensive and luxury items on the one hand, and obsessing about food on the other.
A good rule of thumb is simplify, simplify, simplify. Be frugal - and what you save in grocery monies contribute to our food bank or Deborah’s Place or Pacific Garden Mission or another worthy cause. Cut back on quantity, which is to say don't take second helpings, leave the table satisfied but not stuffed, don't over-eat in order to make up for not eating the things you usually eat. Don't feel sorry for yourself and binge on vegan comfort food. Be strict with yourself and do not look at what other people do or don't do.
On the other hand, if you do not fast, do not make it difficult for those who are fasting; be supportive and do not tempt them. Don't justify not fasting or breaking the fast with the argument that hospitality trumps fasting.
Hospitality is an attitude, not a meat-platter, and can be expressed in vegetarian and vegan terms as well as carnivorous ones! It is quite possible to have a wonderful time without, for example, meat or booze (and if you can't have a wonderful time without them you have a very serious problem).
Finally - if your doctor told you that you must go on a vegan diet for a while - or if your personal trainer put you on such a regime to help get you in shape - no one would say boo or second guess what you were doing. Why then do we sometimes find such an unwillingness to accept fasting as the time-honored, biblical and traditional, and widely practiced spiritual discipline it is? Sometimes we know that something is right when there is such self-justifying resistance...
But the short answer to how should we fast is: with a light heart and a serious purpose, glorifying God for the opportunity! (Fr. John)