She met a famous singer and was beside herself with joy.
Literal
She [topic-は] famous singer [to-に] met, happy-and self [object-を] forgot.
我を忘れる (われをわすれる, 'to forget oneself, to be beside oneself') is an idiom for being overwhelmed by emotion. うれしくて provides the reason in te-form — 'being happy, [she] forgot herself.' A vivid expression of emotional intensity.