。
She sent a telegram saying she was coming.
Literal
She [topic-は] come [quotative-と] telegram [object-を] sent-came.
電報を打つ (でんぽうをうつ, 'to send a telegram') is the fixed expression — 打つ ('to strike') refers to the original telegraph key. 打ってきた uses ~てくる meaning the telegram arrived toward the speaker. A somewhat dated reference — telegrams are rarely used now.