The quick answer: I'd read the Shakespeare first. Cliff's Notes will tell you "Lear appears on stage with dead Cordelia in his arms, yelling," whereas Shakespeare will lead up to such an impacting moment with grace, suspense, and solemnity.
What I would advise you to do if you need some help with the language, though, is to get yourself an edition of the Shakespeare play you're interested in that has significant commentary. There are dozens of different editions of each play out there, and many will 'sum up' what is happening in a scene either in the margins of the text or in the introduction to each new scene. It will be up to you to decide what level of editorial assistance you might need, whether you're brand-new to Early Modern English and you'll look for a high school edition of the play (such as Macmillan or Penguin), undergraduate (Norton or Broadview), or graduate (Oxford, New Cambridge, Arden).
MOST IMPORTANTLY, though, DON'T TRUST the Cliff's/Coles' Notes for assignments! Most of the time, they will get the plot of the play down correctly, but if there were any way to make what Shakespeare was thinking any clearer, he would have written it differently. In sticking to the Coles' Notes, you will miss out on a lot of the double-meanings, symbols and images that make Shakespeare as famous as he is. I read over the Hamlet notes for his "to be, or not to be" soliloquy recently, and there were volumes of meaning that a teacher would hope you'd pick up on that were completely absent from the translation. It told you literally what Hamlet's words MEANT, but not what he was really saying.