In The Annotated Alice, Martin Gardner provides background information for the characters.
The members of the boating party that first heard Carroll's tale show up in Chapter 3 ("A Caucus-Race and a Long Tale").
Alice Liddell herself is there, while Carroll is caricatured as the Dodo (because Dodgson stuttered when he spoke, he sometimes pronounced his last name as Dodo-Dodgson).
The Duck refers to Canon Duckworth, and the Lory and Eaglet to Alice Liddell's sisters Lorina and Edith.

Bill the Lizard may be a play on the name of British Prime Minister Benjamin Disraeli.
One of Tenniel's illustrations in Through the Looking-Glass—the 1871 sequel to Alice—depicts the character referred to as the "Man in White Paper" (whom Alice meets as a fellow passenger riding on the train with her) as a caricature of Disraeli, wearing a paper hat.
The illustrations of the Lion and the Unicorn (also in Looking-Glass) bear a striking resemblance to Tenniel's Punch illustrations of Gladstone and Disraeli as well.

Gardner has suggested that the Hatter is a reference to Theophilus Carter, a furniture dealer known in Oxford, and that Tenniel apparently drew the Hatter to resemble Carter, on a suggestion of Carroll's.
The Dormouse tells a story about three little sisters named Elsie, Lacie, and Tillie.
These are the Liddell sisters: Elsie is L.C. (Lorina Charlotte); Tillie is Edith (her family nickname is Matilda); and Lacie is an anagram of Alice.

The Mock Turtle speaks of a drawling-master, "an old conger eel," who came once a week to teach "Drawling, Stretching, and Fainting in Coils."
This is a reference to the art critic John Ruskin, who came once a week to the Liddell house to teach the children drawing, sketching, and painting in oils. (
The children did, in fact, learn well; Alice Liddell, for one, produced a number of skilful watercolours.)

The Mock Turtle also sings "Turtle Soup."
This is a parody of a song called "Star of the Evening, Beautiful Star", which was performed as a trio by Lorina, Alice and Edith Liddell for Lewis Carroll in the Liddell home during the same summer in which he first told the story of Alice's Adventures Under Ground.
In The Annotated Alice, Martin Gardner provides background information for the characters. The members of the boating party that first heard Carroll's tale show up in Chapter 3 ("A Caucus-Race and a Long Tale"). Alice Liddell herself is there, while Carroll is caricatured as the Dodo (because Dodgson stuttered when he spoke, he sometimes pronounced his last name as Dodo-Dodgson). The Duck refers to Canon Duckworth, and the Lory and Eaglet to Alice Liddell's sisters Lorina and Edith.
Bill the Lizard may be a play on the name of British Prime Minister Benjamin Disraeli. One of Tenniel's illustrations in Through the Looking-Glass—the 1871 sequel to Alice—depicts the character referred to as the "Man in White Paper" (whom Alice meets as a fellow passenger riding on the train with her) as a caricature of Disraeli, wearing a paper hat. The illustrations of the Lion and the Unicorn (also in Looking-Glass) bear a striking resemblance to Tenniel's Punch illustrations of Gladstone and Disraeli as well.
Gardner has suggested that the Hatter is a reference to Theophilus Carter, a furniture dealer known in Oxford, and that Tenniel apparently drew the Hatter to resemble Carter, on a suggestion of Carroll's. The Dormouse tells a story about three little sisters named Elsie, Lacie, and Tillie. These are the Liddell sisters: Elsie is L.C. (Lorina Charlotte); Tillie is Edith (her family nickname is Matilda); and Lacie is an anagram of Alice.
The Mock Turtle speaks of a drawling-master, "an old conger eel," who came once a week to teach "Drawling, Stretching, and Fainting in Coils." This is a reference to the art critic John Ruskin, who came once a week to the Liddell house to teach the children drawing, sketching, and painting in oils. (The children did, in fact, learn well; Alice Liddell, for one, produced a number of skilful watercolours.)
The Mock Turtle also sings "Turtle Soup." This is a parody of a song called "Star of the Evening, Beautiful Star", which was performed as a trio by Lorina, Alice and Edith Liddell for Lewis Carroll in the Liddell home during the same summer in which he first told the story of Alice's Adventures Under Ground.
Alice's Adventures in Wonderland