The full quote is as follows: "Who controls the past, controls the future: who controls the present controls the past."
In your question you ask how the quote shows the people of Oceania struggling to control the past. I actually don't think it does and I don't think the pages around it do either.
The quote argues that the government's control of what people believe about the present allows it to control both the past and the future. But no one other than Winston seems to be fighting back against the lies and even he is only doing it in his own mind.
We know that Winston remembers facts that don't match up with the official histories, but we don't see anyone else struggling like he does.
Winston's job in the Ministry of Truth is to censor, revise, spin, delete, and destroy the past. He recycles stories and turns people into unpersons. It's a satire of what most newspapers and tabloids do, even in first-world democracies today.
You've heard the sayings "Same old story" and "No news is good news." All you need is a montly subscription to the newspaper to last you a lifetime, because only the facts change, not the stories. Bad news dominates: "If it bleeds, it leads." And the readers become numb to it. In this way, the past is never the past. It becomes the future. After repeating itself so often, it never was.
The Ministry of Truth has people of Oceania completely confused. They don't even know what year it is. They don't know who their enemy is. One day it's Eurasia and the next it's Eastasia. Usually, countries use this kind of misinformation and disinformation against their enemies in war, but Oceania uses it against their own people--to keep them quietly supportive and productive during the war.
Examine Orwell's satire:
By 2050—earlier, probably—all real knowledge of Oldspeak will have disappeared. The whole literature of the past will have been destroyed. Chaucer, Shakespeare, Milton, Byron—they’ll exist only in Newspeak versions, not changed into something contradictory of what they used to be. Even the literature of the Party will change. Even the slogans will change. How could you have a slogan like ‘freedom is slavery’ when the concept of freedom has been abolished? The whole climate of thought will be different. In fact there will be no thought, as we understand it now. Orthodoxy means not thinking—not needing to think. Orthodoxy is unconsciousness.
It's all part of a cyclical counter-intelligence campaign against the proles to keep the Inner Party in power. The proles become slaves to the truth through their ignorance. The less they think, the more they work.
So says eNotes:
By denying the individual access to accurate information of current events and history, the Party is taking away his or her power to make decisions based on what is happening in the world around him, as well as what has happened in the past. To learn from the mistakes of the past, as well as benefit from its wisdom, the average citizen is thus able to effectively evaluate the state. As the saying goes, “History is bound to repeat itself.” By rewriting history into that which has never happened, Big Brother is preventing history from thus repeating itself. By controlling the past, he thus controls the future.
Henry Ford said, "History is bunk." Those who cannot remember the past are doomed to repeat it.
There is a fundamental problem in the question: do the people of Oceania struggle for control of the past?
They do not. The quote shows how the Party can effectively control the population, and there is no indication, with the exception of Winston, in the book, that shows an attempt at controlling the past from the people as they are shown to accept.