Learn Hardcore Latin: Puella in litore concham albam invenit et matri ostendit. - The girl finds a white shell on the shore and shows it to her mother.

Because puella is in the nominative case, which is the case normally used for the subject in Latin. The ending -a here is the nominative singular ending of a first-declension noun.

So puella means the girl as the one doing the actions.

Why is it in litore and not something like in litus?

After in, Latin uses different cases depending on the meaning:

in + ablative = location, meaning in / on / at
in + accusative = motion into or onto something

Here the girl is already on the shore, so Latin uses the ablative: litore.

Also, the dictionary form of this noun is litus, litoris (a third-declension neuter noun), and its ablative singular is litore.

Why do both concham and albam end in -am?

Because concham is the direct object of invenit, and albam is an adjective describing concham. Latin adjectives must agree with the nouns they describe in:

gender
number
case

So if concham is , then must also be .