The trees have started to bud.

Literal

Trees [topic-は] buds [object-を] bring-out began.

芽を出す ('to put out buds') is the verbal collocation for budding — literally 'to bring out buds.' Pairs with intransitive 芽が出る and the more poetic 芽を吹く. ~始める attaches to verb stems for 'begin to X.' The kanji-doubling 木々 with the iteration mark 々 marks the plural 'trees' — a productive pattern Japanese uses for a small handful of nouns (人々, 山々, 国々).