I can see why you are having a hard time! The essay is very densely written, with lots of long sentences. That it is online, rather than on paper, compressed into such a tight space, makes the task even more difficult, as there are more line breaks than there would be in a standard page layout.
Sean's idea is good. Go sentence by sentence until you understand each, jotting down your understanding of what each sentence means in short, simple sentences.
Joyce's paragraph-long first sentence, for example, probably could be broken into four or six short statements.
Another thing you can do when you don't understand a text is to Google the name of the author and the title of the text to see what (if anything) others have written about it. This can't substitute for your own reading, but it can sometimes help to see how other people have understood what you are trying to understand.
Another problem is that Joyce's essay is extremely erudite, making reference to all manner of events and characters from other pieces of literature. Use Wikipedia or a similar source to get a quick idea of what Joyce means when she refers to some character or mythical figure you've never heard of.
Concentrate on the beginning and the end, remembering that most essayists introduce their main theme at the beginning and/or summarize their main theme at the end. For sure, the most important things are almost always at the beginning or the end, with the body of the essay reserved for arguing and proving the points that the essayist is making. It's okay if you don't grasp every nuance of the body paragraphs so long as you understand the primary message(s) of the essay.
If you want to post your own summary here, for us to compare against the original, please do!
Simone, EssayForum.com