Pigeon parents feed their young on what is termed 'pigeon milk'. This is not anything like dairy milk, although it is of the same color and consistency.
Baby pigeons can be fed on Kaytee Exact Baby Formula, Egg Food, Natural Flavoured Complan (available in the UK) , or Chick Crumbs that have been soaked in hot (not boiling) water for half an hour, blended and passed through a sieve. In an emergency they can be fed puppy biscuits that have been soaked until they are fluffy.
Unlike other birds, baby pigeons do not gape to be fed. The flutter their wings and squeak, and then are 'pumped' food from the parent birds' crops.
Very young pigeons will have to be fed by syringe or tube.
You can feed an older 'baby' pigeon gently opening its beak and inserting the soaked biscuits.
You can make a paste of egg food, putting it in one of those disposable bags used for piping icing. Gently force the pigeons beak open and squeeze some of the paste in slowly. Allow it plenty of time to swallow. Or you can soak the egg food, leave it to stand and then make pellets out of it which can be fed as described above for puppy biscuits.
This link is to web pages on tube feeding adult & baby pigeons: Tube Feeding a Pigeon . A simple method of feeding a very young baby pigeon (even just a couple of days old) is the Cut off syringe method!