Great question. I would simply suggest reading all the classic novels that are hallmarks in English literature. Aside from Shakespeare, there are plenty of good authors: Dickens, Austen, Melville, Poe, Hemingway, Faulkner, the Bronte sisters, Fitzgerald, Chaucer, Steinbeck, and many others
By doing this, you’ll know each writer’s voice and how their works contributed to the literature on their merit. To know their writing style, you have to know the devices they’ve used like alliteration, assonance, flashback, first or third person-narration, in media res, etc.
Overall, be well-read and know all literary and rhetorical devices to heart.
And also read up on the author’s life and biography to know his or her mindset and the historical context in which their work was written. That helps in establishing what the hidden meaning or theme is behind the literary work.
Look for any symbolism or meaning behind the story; in other words, look for what you get out of reading the work.
Another way to get at theme is to look at how the characters interact and their development. Usually, characters have an arc that serves the story and therefore the themes.
Dialogue also helps offer insight into the characters as well (by how they speak can show where they’re the form or their backstory).
Also, keep an eye on how the writers write the story’s environment or setting and how they construct the plot of the story: the pacing and what devices the author uses to keep the reader’s interest. There’s also tone or what the atmosphere of the story is like (sad, dark, optimistic, etc.)
Lastly, I would also suggest reading literature reviews from critics and scholars to see what their thoughts and see whether their observations line up with yours in order to have an overall understanding of the writer and their work.
Hope this helped.