Noun: bother, inconvenience; ailment.
Vaiva appears in our example in the abessive case singular, abessive case expressing the lack or absence of the marked noun. In English, the corresponding function is often expressed by the preposition without or by the suffix -less. So vaivatta means ”without bother.” Abessive case is rarely used in speech or writing except in certain expressions.
Let’s translate the whole musical title, Miten menestyä vaivatta liike-elämässä, which is the Finnish translation of the American book and subsequent musical, ”How to Succeed in Business Without Really Trying.”
Miten means ”how.”
Menestyä is a verb meaning ”to succeed” or ”to be successful.”
Liike-elämääsä is a compound term which means ”business world.”