She complained to the manager that the service was poor.

Literal

She [topic-は] manager [to-に] service [subject-が] bad [quotative-と] complaint [object-を] said.

苦情を言う ('to file a complaint') is the standard collocation for formal complaining — slightly more measured than the colloquial 文句を言う. The embedded clause サービスが悪い ('the service is bad') is reported through quotative と. サービス is a katakana loanword that has fully naturalized in Japanese — used for hospitality service, customer service, 'free' (in Japanese conversational sense, e.g. これ、サービスです 'this is on the house'), and many other senses.