In Dungeon Crawl Classics, the known spells for wizards and elves are for the most part randomly generated for each character.
How do clerics determine their own known spells?
An ideal answer would cite the rules as written.
Page 31, Table 1-5 says a 1st level cleric knows 4 1st level spells. The rest is up to the Judge. In some campaigns the spells are given by the god as he or she sees fits, in others, the Judge may let the cleric pick their spells and if anything sounds out of a god's domains, they may veto that spell. And some, like me, prefer to roll those spells for both wizards and clerics.
For wizards, they learn them randomly (page 48):
Known spells are determined randomly (see Chapter 5: Magic). They may be of any level for which the wizard is eligible, as shown by the max spell level column.
But there is no such rule for cleric characters.
I believe that they are supposed to be rolled for.
I couldn't find any text specifically explaining this, but the "Number of Spells Known" stat on Clerics, the table of Cleric Spells being formatted in the same manner as the table of Wizard Spells, and the inherent randomness of Dungeon Crawl Classics in general leads me to believe that this is the intention of the authors.