How does George shows the theme of dream in Of Mice and Men?
In Of Mice and Men, George is the figurative glue that holds the dream together, and makes the dream at least a little bit plausible, or likely.
Lennie, Candy, and Crooks have no chance of ever pulling off something like buying their own places and being their own bosses. George makes the possibility at least a little bit credible.
Interestingly, though, in terms of George showing the American Dream, as you ask about, George is the one who tries to keep his dream quiet. Lennie isn't supposed to tell anyone else, but of course, Lennie being Lennie, he tells anybody that will listen.
The novel begins and ends with George and Lennie talking about their dream, and that's the main method in the novel of raising the issue of the American Dream. Notice, though, that in this case it is just a small dream. They have no grand illusions about becoming wealthy or anything, they just want a little piece of the metaphorical pie. Even that, however, proves to be illusion, though it is not grand.
George shows the idea of dreams, or the American Dream, quite well (especially in conjunction with his friend Lennie).
Think about what George is doing in this book. During the whole book, he has this dream that he shares with Lennie. He is always talking about this dream of his.
George's dream is a little more mature than Lennie's. Lennie's is focused on petting rabbits. But George's is the real American Dream, I think. His dream is centered around being his own boss and doing what he wants when he wants to -- at his own pace.
So, to me, that's how George shows this theme -- by having this dream that he holds onto throughout the whole book.