I find the only way to really understand Joyce in a significant way beyond the beauty of his prose is to read up on the political and religious background of Joyce’s Dublin.
There’s a terrific Annotated Joyce book which fills in the many blanks of The Dubliners and A Portrait of an Artist as a Young Man. It is an academic imperative to understand some of the history behind Irish politics of the 19th century, Parnell in particular and the events surrounding the Potato Blight and English estate agents for absentee landlords and early 20th century and some of the Catholic references when reading Joyce if you want more than an impressionistic or superficial reading of these novels.
When tackling a mammoth full of beauty, whim and occasional gobbledygook such as Ulysses or Finnegan’s Wake, I suggest reading an annotated companion to the books! It’s worth the effort. There is also a fabulously entertaining and interesting free podcast by Irish writer Frank Delaney called Re:Joyce in which he dissects a page of Ulysses for each five minute show. It is often humorous and the anecdotes and history lend rich details to Joyce’s difficult book.
A decent background skim of the Greco-Roman classics and the literary canon or the “Western Canon” is very useful as well. I like Harold Bloom’s collection of Canons from various ages and eras.
Obviously that is an immense amount of reading and disseminating. Therefore, I suggest reading a summary of the canon with highlights of the Hellenistic period, etcetera to follow the references and allusions to the myths and the gods in Joyce’s work.
Spark notes and cliff notes and the Cambridge Reader to Joyce are also exceedingly helpful shortcuts to peering a little closer into his work.
At the end of the day reading and learning is a gradual process which enriches our lives slowly over a whole lifetime.
I am currently embarking on a re-read of A Portrait of An Artist as a Young Man after reading it years ago as a teenager. I know I will have a different experience having read and lived much in the years between falling into the pages. And I’m going to have my study guides and annotations at hand for a heavier, more in the know experience. The prose and the spiritual approach to art and history and human psychology affected me deeply in my extreme youth and I expect some of that will still be there within me along side the more powerful notions of understanding the social, cultural, historical and religious contexts of the world of Joyce’s books.
Nationalism in James Joyce’s work; http://mural.uv.es/romoma/nationalism.htm
Irish Mythology (very important to Joyce’s writing)
The Myths of Stephen Dedalus http://m.voices.yahoo.com/the-myths-stephen-dedalus-james-joyces-portrait-2666810.html
Celtic and Irish Mythology and Folklore in the fiction of James Joyce http://digitalcommons.mcmaster.ca/cgi/viewcontent.cgi?article=4667&context=opendissertations