How many spells can a Cleric learn?
None, because Clerics 'Prepare' their spells without having to learn them.
Clerics, Paladins, and Druids are unique spellcasters in that, unlike every other spellcaster, they do not learn a certain number of spells per level up. This means that they have the entire list of spells to work from. A cleric doesn't learn any spells mechanically, but they do prepare them, which means they do not have to learn them as they gain levels. The process of preparing spells is detailed in the PHB on page 58:
... you prepare the list of cleric spells that are available for you to cast, choosing from the cleric spell list. When you do so, choose a number of spells... The spells must be of a level for which you have spell slots.
(The cleric spell list it mentions is found starting on page 207.)
A 1st level Cleric can prepare a number of spells from the full list of 1st level spells equal to their Wisdom Modifier + Cleric Level per day. Once a Cleric, Druid, or Paladin reaches the proper level to gain 2nd level spell slots, again they can prepare spells from the full list of 2nd level spells. (The same section on page 58 gives a good example of a level 3 cleric, who has 1st and 2nd level spell slots.) You can then change your list of prepared spells in between long rests, which makes Clerics, Druids, and Paladins very versatile with their spells, as they can be changed to suit the needs of the party.