There are many things that make Shakespeare's writing complex to modern readers. First, especially for high school students, is the fact that the plays were written 400 years ago, and while that technically still qualifies as Modern English, it is by no means the same English we hear and speak each day. Shakespeare created new words all the time; he took words people knew and then changed the form into a different part of speech (ex. he might use the noun 'brain' but then use it as a verb meaning 'think); he used words that meant one thing then and a different thing now, or the word has fallen out of use altogether.
Another aspect that is challenging is that he is writing in blank verse -- unrhymed iambic pentatmeter. While the intent of the verse is be like regular speech, it is more elevated than we speak. The demands of the meter affect the line in terms of word choice, word order, and syntax, which can complicate the reading.
Shakespeare also had some very profound insights into human nature and how humanity handles the ups and downs of life. Because he is rather philosophical, his subject matter can become more challenging all by itself, and then is seemingly more complicated by the language issues mentioned above.
My most simple advice to you is to read it aloud to yourself and don't stop reading until you get to a piece of END punctuation, such as a period, question mark, or exclamation point. If you read for complete thoughts (whole sentences) it is much easier to understand than if you try to understand parts of sentences such as a single line or two. Rarely does Shakespeare have a complete sentence in a single line, but when you read like that you lose the complete context of any part of his thought and then you lose the meaning.