。
She was beside herself with joy at the news.
Literal
She [topic-は] that news [object-を] hearing [then-て] self [object-を] forgot [then-て] rejoiced.
我を忘れる ('to lose oneself') in te-form chains into 喜ぶ ('rejoice'): she lost herself, and rejoiced. The combination captures rapture — joy so overwhelming that ordinary self-awareness goes out the window, the same trance-state described as 'beside oneself' in English. 喜ぶ is the standard verb for expressing joy, derived from the i-adjective 嬉しい ('happy') via the same emotion-verb derivation that gives 悲しい→悲しむ. The whole sentence has a slightly literary tone, the kind you'd find in fiction or memoir.