Ask your GM; "you learn its properties and how to use them"
The quote above is from the identify spell.
"Property" is defined as:
An attribute, quality, or characteristic of something.
But the interpretation of this phrase would be entirely up to a GM because what count as "an attribute, quality, or characteristic" of a Deck of Many Things is up to interpretation.
This is effectively identical to the section on "Identifying a Magic Item":
The identify spell is the fastest way to reveal an item’s properties. Alternatively, a character can focus on one magic item during a short rest, while being in physical contact with the item. At the end of the rest, the character learns the item’s properties, as well as how to use them.
Showing again, that the interpretation of this phrase is up to the GM (this wording is found in the DMG after all).
My personal interpretation:
You learn a property if and only if you can actually use it.
You can use a property if and only if you can specifically choose for it to occur.
Therefore you do not learn what each card does because you cannot select a specific card.
You do not learn how many cards are ordinarily in a deck because this is not something you have control over.
You do not learn which cards are in the deck because this is not something you can specifically choose to have happen (which card(s) are in the deck is random).