Both Beckett and Joyce were Irish, but they met in Paris (where he moved in 1920 and stayed for about twenty years). They were both writers, athough Joyce is most know for his novels, like "Ulissess", and Beckett for his plays, like En attendant Godot (english: Waiting for Godot)
Mr Joyce dictated him parts of the "Finnegans Wake". Beckett also translated a fragment of the book into French under Joyce's supervision. There are varying opinons about if Beckett was a Joyce's secretary or not.
Samuel Beckett wrote essay on James Joyce, entitled "?". Other his writing could be influenced by his friend,
fellow Irishman James Joyce.
Interesting fact: it seems that Lucia Joyce, daughter of James, fall in love with Samuel, who unfortunately (for her) didn't want her.
Quote on Joyce:
James Joyce was a synthesizer, trying to bring in as much as he could.
I am an analyzer, trying to leave out as much as I can.