Hennes bøker står på en hylle nær trappen.

Hennes is the third-person feminine singular possessive pronoun – basically “her.” Unlike English, you don’t add ’s to a noun. You simply place hennes before the noun:
• hennes bok – her book
• hennes hus – her house
For a male possessor you use hans (his), and for “their” you use deres.
If you want to make the noun definite in Norwegian, you usually move the pronoun after the noun:
• boka hennes – the book of hers (the book that belongs to her)

Bøker is an indefinite plural form. Norwegian has no separate indefinite article (like “a”) in the plural. You can add noen (some) if you want emphasis, but it isn’t required, especially with a possessive pronoun:
• hennes bøker – her books (indefinite, simply those books of hers)
If you did say noen bøker, that would mean “some books” in general, without necessarily implying they belong to her.

Use the noun in the definite plural and attach the pronoun after it:
• bøkene hennes – the books of hers / the books that belong to her

På is used for placing things on surfaces or open structures. A shelf (hylle) is treated like a surface: you put things on it.
• på en hylle – on a shelf
By contrast, i (“in”) is used for enclosed spaces or containers (e.g. i en boks – in a box). You will sometimes see i en bokhylle (“in a bookcase”) because a bookcase can be thought of as a cabinet, but simple shelves take på.

Nær is a preposition meaning “near” or “close to.” If you refer to a specific staircase, you use the definite form trappen (“the staircase”).
• nær trappen – near the staircase (that we both know about)
If you meant any staircase in general, you’d say nær en trapp – near a staircase. Another common alternative is ved trappen – by the staircase.

In a normal Norwegian main clause you follow Subject-Verb-Adverbial order:
• Hennes bøker (S) står (V) på en hylle nær trappen (Adv).
You can move the location phrase to the front for emphasis, but you must still respect the V-second rule (the finite verb remains in slot 2):
• På en hylle nær trappen står hennes bøker.
Here på en hylle nær trappen is first, står stays second, and the subject hennes bøker follows.