Much of the humor in Great Expectations comes from Dickens's detailed descriptions of his larger-than-life characters. For instance, Uncle Pumblechook is described as "a large, hard-breathing, middle-aged, slow man, with a mouth like a fish, dull staring eyes, and sandy hair standing upright on his head." Mr. Wopsle, for his part, is described as a man who has "united a Roman nose and a large shining bald forehead." The relationship between Joe Gargery and Mrs. Joe also generates more than its fair share of humor. Poor old Joe is so scared of his domineering wife that he secretly offers gravy to Pip during Christmas dinner as if it were some sort of illicit or criminal act.

There is much situational irony in the earlier chapters. For instance, Estella likes to put on airs and graces, believing herself destined for a life as a lady of quality. In reality, she's the daughter of a gypsy and a convict. A more humorous variety of irony comes in the shape of Matthew Pocket, who writes books advising parents on how to raise their children but has no time for his own kids.

I will give you two examples of both irony and humor, in chapters 1 and chapter 2.

Pip’s encounter with the convict in chapter 1 is full of irony and humor.  All of the irony does not become apparent until later, when we find out the full effect of this terrifying event.  The event that defines Pip’s childhood also defines his adult life, since Magwitch sends him the money for his “great expectations.”  Although Pip is frightened, the reader’s reaction is more humor.

Another example of both humor and irony is Tickler in chapter 2, the name for Mrs. Joe’s cane. 

Tickler was a wax-ended piece of cane, worn smooth by collision with my tickled frame. (ch 2)

The name Tickler is very ironic, and some might find it funny (although it is bitter humor) that the cane would be named Tickler.