I still remember my first encounter with the Bard. I was a tender seventh grader staring down Othello. To be frank, I was expecting to be confused and bored out of my mind, but once I figured out what was going on, I fell in love with Shakespeare and became quite addicted to his dramatic plots, epic language, and remarkable characters.
However, I know that the biggest barrier with Shakespeare for many people is the language. And, as lovely as I think Shakespeare's work is, I'd be lying if I said reading Elizabethan English is easy. It isn't - on the first try. It's a mistake to try to bulldoze through Shakespeare's work. If you want to appreciate Shakespeare's work, you must understand it. And if you want to understand it, you're going to need to do more than just battle your way blindly through the play. I believe the best way to approach Hamlet (or any Shakespearean play) is the way Shakespeare's original audience did, a form of method reading, if you will.
Shakespeare's audiences were familiar with these stories before he ever wrote them (Yep. Shakespeare's ideas were all adaptations. He'd win Best Adapted Screenplay at the Oscars, not Best Original.) Therefore, before you try to dive into Shakespeare, you need to be familiar with the story behind Hamlet, or whichever play it is you're reading. I usually object to reading summaries before reading a book, but with Shakespeare it is essential. Read a good thorough summary of the plot and use a side-by-side modern translation (No Fear Shakespeare) as a supplement (but not as a substitute! Sorry, you really need to read both the original and the translation. Do not just read the modern version and skim the original text) to help you figure out what's going on.
In Shakespeare's time, people didn't ask if you wanted to see a play. They asked if you wanted to hear a play. And hearing Shakespeare's work performed is vital - you'll pick up nuances and intonations you can't pick up by reading. Once you know the story and characters, you need to either see or hear Shakespeare performed. If you're like me and live nowhere near a good theater (let alone Shakespeare repertory company), you're going to have to rely on films or audio recordings. I've heard the best Hamlet film is the Kenneth Branagh version. (Alas! I hath never lain mine eyes upon it, but I have watched the Laurence Olivier and Mel Gibson versions. Both are well-acted, but cut out essential subplots.) One thing though: if you watch a film adaptation, you're not going to do yourself much good if you watch one of the modern ones with modern dialogue. You want to hear the dialogue in its original; otherwise, you're defeating the purpose of watching the movie. (Don't get me wrong. I am not saying do not watch the modernized versions, just do not think that that will help you appreciate the dialogue. Besides, Hamlet is not Hamlet, to me, unless he's wearing tights and emoting, "Fie on 't," but that's just a personal opinion.)
A good alternative is listening to unabridged audio books of Hamlet and following along with the text. (I love the one performed by Frank Muller. He gives each character a distinct voice, especially the pompous windbag Polonius. I also couldn't believe how moving some of the scenes were and I wasn't even watching anything. I, ahem, got teary-eyed during Hamlet's first soliloquy) Whichever route you choose, the main thing is listening to Shakespearean dialogue performed by someone who knows what they're doing. You will not believe what a difference listening to a talented, well-trained actor delivering a properly intoned monologue is over listening to one of your classmates mumbling through (and utterly butchering) a monologue. In skilled hands, Shakespeare's dialogue (and that mysterious iambic pentameter) jumps off the page and comes to life, as Shakespeare intended.
Then after you know the story and have heard Shakespeare from capable hands, then (and only then) read the play. I think you'll find your experience much more enjoyable and much less frustrating. Good luck!