Anna zet een strandstoel op het strand.

Both op het strand and aan het strand can be heard, but they focus on slightly different ideas:

• Op het strand emphasizes the surface you stand on (“on the sand”).
• Aan het strand emphasizes proximity to the beach (“by the beach”).

In this sentence, because Anna literally places the chair on the sand, op is the best choice.

Dutch has two grammatical genders for nouns: de-words (common gender) and het-words (neuter).

• Strand is neuter, so it takes het.
• Stoel is common gender, so it takes de.
  When you form a compound noun, the gender/article of the compound is that of the last element, here stoel, so de strandstoel.

Dutch has separable verbs like opzetten (“to put on” clothing or “to set up” equipment). You distinguish them because in a separable-verb construction the particle op splits off and attaches directly to the finite verb:
– “Anna zet de tent op.” (Here zet … op is the separable verb opzetten, “sets up the tent.”)

In our sentence, however, op is followed by het strand, so it’s functioning as a preposition, not the verb particle. The verb itself is simply zetten.

The neutral order in Dutch main clauses is Subject–Verb–Object–Adverbial:
Anna (S) zet (V) een strandstoel (O) op het strand (Adv).

You can front other elements for emphasis, e.g.:
– Op het strand zet Anna een strandstoel. (Emphasizes the location.)
But then you must keep the verb in second position.

They all mean “to put down,” but with nuances:

• Zetten often implies placing something upright.
• Leggen implies placing something down flat (→ “to lay”).
• Plaatsen is more formal/general: “to place” or “to position.”

A chair stands upright, so zetten is most natural here.