。
The lovers wandered around the field looking for wild strawberries.
Literal
Lovers [topic-は] wild-strawberries [object-を] searching field [object-を] here-and-there walked-around.
野苺を探して uses the て-form to express manner ('while searching for / in search of'), tying the searching to the wandering. あちこちと is an adverbial expression — 'here and there' — and the と here is the adverbial と that often follows mimetic and adverbial expressions to mark manner. 野原を歩き回る takes the field as a direct object via を, the standard pattern for verbs of moving over a path or area.