What happens to Boxer and how do the other animals learn of his fate? How do they come to a final conclusion about these events?

Boxer is the most tragic character in the book. He is hardest working animal and he does genuinely believe in the revolution. His mottos are famously, "I will work harder," and "Napoleon is always right." 

As to what happens to him, there are two storylines. 

First, according to Napoleon, he is taken to this animal hospital and taken care of before he dies. He was cared for, loved, and honored. Napoleon is obviously lying to make himself look better. 

Second, there is what really happened, which is intimated early on when Old Major predicts what Jones will do:

You, Boxer, the very day that those great muscles of yours lose their power, Jones will sell you to the knacker, who will cut your throat and boil you down for the foxhounds.

After Boxer serves the farm with all his might and grows ill and cannot continue to work, Napoleon sells Boxer to the Knackers, where he will be made into glue. This shows that Napoleon is brutal and cruel. Here is the whole text, which shows the greatness of the tragedy.

The animals crowded round the van. ‘Good-bye, Boxer!’ they chorused, ‘good-bye!’

‘Fools! Fools!’ shouted Benjamin, prancing round them and stamping the earth with his small hoofs. ‘Fools! Do you not see what is written on the side of that van?’

That gave the animals pause, and there was a hush. Muriel began to spell out the words. But Benjamin pushed her aside and in the midst of a deadly silence he read:

‘Alfred Simmonds, Horse Slaughterer and Glue Boiler, Willingdon. Dealer in Hides and Bone-Meal. Kennels Supplied.’ Do you not understand what that means? They are taking Boxer to the knacker’s!’