Çiftçi tarlada taze sebze dikiyor.

The suffix -da is the locative case marker meaning “in/on/at.”
tarla (field) + -da → tarlada = “in the field.”

In Turkish only definite/specific direct objects get the accusative -(y)i suffix.
Here taze sebze (“fresh vegetables”) is indefinite/general, so it stays unmarked.
If you meant “the fresh vegetables” (specific ones), you’d say taze sebzeyi dikiyor.

dikiyor consists of the root dik- (“to plant,” “to erect”) + the present continuous tense suffix -iyor for third-person singular.
So dikiyor = “he/she/it is planting” (or “plants” in a habitual sense).

Both verbs can mean “to plant/sow,” but:
• ekmek is generally “to sow seeds” (grains, cereals).
• dikmek is “to plant seedlings, young plants, trees.”
Since vegetables are often transplanted as seedlings, dikmek is more natural here.

Turkish does not use separate words for “a” or “the.”
• Indefiniteness/definiteness is shown by context or, for objects, by the accusative -i suffix.
• Subjects and nouns stand alone without an article.

Turkish adjectives always precede the noun they modify and do not agree in number or case.
So taze (fresh) comes before sebze (vegetable), making taze sebze.

The default order here is:
Subject – Locative adverb – Object – Verb
Çiftçi (S) tarlada (locative) taze sebze (O) dikiyor (V)
Turkish word order is fairly flexible, but the verb usually comes last.

tarla specifically means a cultivated field used for farming or agriculture.
alan is a more general term meaning “area,” “space,” or “open ground.”