I'll start you off with one quote from chapter one from Steinbeck's Of Mice and Men. On page 15 in my edition George retells Lennie about the house, etc., that they will one day have:
"O.K. Someday--we're gonna get the jack together and we're gonna have a little house and a couple of acres an' a cow and some pigs and--"
"An' live off the fatta the lan'," Lennie shouted. "An' have rabbits. Go on, George! Tell about what we're gonna have in the garden and about the rabbits in the cages and about the rain in the winter and the stove, and how thick the cream is on the milk like you can hardly cut it. Tell about that, George."
This introduces the constant theme in the novel of workers dreaming of owning their own places. Notably, the workers, including Lennie and George here, do not dream of being millionaires or anything so grandiose. They simply dream of owning a little land and a little place and of being their own bosses.
George will describe this dream to Lennie repeatedly in the novel, Lennie will tell it to others, even when he's not supposed to, and Crooks and Candy will want to join in. The American Dream, or the illusion of it, is central to the work.
I'll get you started, but I think you're fully capable of getting a few yourself.
Just to make sure you understand what you're looking for, within the context of OMAM, is that America holds endless possibilities. In the words of James Truslow Adams in his book The Epic of America:
The American Dream is "that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is not a dream of motor cars and high wages, but a dream of social order in which each man and each woman shall be able to achieve the fullest stature of which they are capable of, and be recognized by others for what they are, regardless of the circumstances of birth or position.
If we take a look at George, when he reflects on what he and Lennie will have, he is expressing the possibility of the American dream:
Well,' said George, 'we'll have a big vegetable patch and a rabbit hutch and chickens. And when it rains in the winter, we'll just say the hell with goin' to work, and we'll build up a fire in the stove and set around it an' listen to the rain comin' down on the roof...'
Given that George and Lennie have a lived a poor live and migrant farm workers, these commodities and comforts will mean a great deal to them.
Think about Lennie's "catch phrase", Crooks's conversation with Lennie in the barn, and you should be on the right track.