I have done this about five times, and had plenty of time to reflect on the experience - so here are some suggestions...
Firstly, it is best to be young - in the teens or early twenties, or else in that state of psychological neoteny which sometimes afflicts academics, scientists and artists. Indeed, I doubt whether it is worth reading James Joyce if you are a mature adult - married, a father, that kind of thing.
Of course I am suggesting that it is worth at least some people reading some of Joyce; and that is because he does what he does very well - and he was a master of language (when he wasn't writing merely to advertise his technique, or to exemplify some tiresome theoretical framework).
But while Joyce's skill as a prose artist is of the front rank, and he took great pains with his writing; as a man he was immature, conceited, pretentious and shallow - so there is a limit to how much one can (or should) get from reading Joyce.
So Ulysses contains some really wonderful parts, and even more pointless, turgid and/ or wilfully obscure stuff (by my interpretation Joyce deliberately deployed obscurity to hide his self-obsessed monomania).
When Joyce is good, he is always writing about himself - in the form of his alter ego Stephen Dedalus. The other characters either serve the goal of elucidating, highlighting, aggrandizing Stephen - or else they are essentially padding (and that stricture includes Leopold Bloom, as well as his wife Molly, insofar as he is not interacting with Stephen).
At root, Ulysses is an episode in the life, in the artistic development, of Stephen Dedalus - who is implicitly the author of Ulysses; Ulysses is 'about' what made it possible to become the man who went-on to write Ulysses.
But, but, but - it is incredibly-difficult/ impossible for the naïve reader to know what the heck is going on in Ulysses.
Therefore, to read Ulysses, you need already to know Stephen - which means you need already to have read the earlier stages of his biography in Portrait of the Artist as a Young Man.
But Portrait of the Artist as a Young Man is also incredibly difficult to understand - therefore you need already to have read its plainly written draft version: Stephen Hero.
(Comparing Stephen Hero with Portrait shows the great increase in Joyce's skill as a writer - but also the degree to which he deliberately used obscurity in order to make his writing seem more impressive.)
So, here is the scheme for How to read Ulysses:
1. Read Stephen Hero. (And if you can't abide Stephen - which would be understandable, stop here.)
2. Read Portrait of the Artist as a Young Man.
3. Read the parts of Ulysses concerned with Stephen; skipping-over the rest.
In fact, just read the first three chapters of Ulysses - which are the best things in the book - and if you don't like them then you may as well give-up at that point and save yourself a lot of pain.
4. If you have liked all of this, then read the rest - why not? But I warn you that much of the second half is both worthless and intensely-annoying - perhaps especially the 'Oxen of the Sun' and 'Circe' episodes.
Sincere Note: Do not, I implore you, attempt to read Finnegans Wake.
You will not succeed; but even if you did you will have wasted your time and energy.
Everything that was bad about Ulysses, and nothing that was good, is put into Finnegans Wake - and amplified to the nth degree.