So quick lowdown on Marxism in general:
Argues that economics is the driving force behind society.
Examine the inequality of class and society (i.e. the power struggle between upper, lower, and middle class, rich vs. poor, owners vs. workers), oppression
So in TGG this can be seen with Gatsby and his struggle to gain power and move higher up the social hierarchy as he is coming from new money , not old like everyone else/ Also the fact that Gatsby knows or feels he must be of a higher position in society so that he can be worthy or approved of Daisy's love? / Can be seen with Daisy and how materialistic she is hence why she stays with Tom / Could make some reference to the Valley of Ashes where Myrtle and George live unhappily trying to get out of the place/ Could compare the life of Daisy to that of Myrtle all because of class and wealth? / Everything in Gatsby and everyone is about money, class and materialism and ultimately without it, you couldn't be apart of TGG world
Hope this helped a bit!