Learn French: Il vaut mieux écouter le tatoueur. - It is better to listen to the tattoo artist.

It comes from the verb valoir, which means "to be worth". The impersonal expression il vaut mieux literally means "it is worth better", but it is the standard French way to say "it is better to..." or "you had better..." when giving advice.

Do I need a preposition like de before the infinitive écouter?

No, the expression il vaut mieux is always followed directly by an infinitive verb. You don't need de or à between them. It is simply il vaut mieux écouter.

Why isn't there a French word for "to" after écouter? In English we say "listen TO the tattoo artist".

In French, the verb écouter (to listen) takes a direct object. This means the action connects directly to the noun without a preposition. You just say écouter le tatoueur, which literally translates as "listen the tattoo artist".

Could I say c'est mieux d'écouter instead of il vaut mieux écouter?

Yes, c'est mieux de + infinitive is also grammatically correct and means essentially the same thing. However, il vaut mieux is a specific, very common set phrase used for giving a recommendation or warning, similar to "it's best to" or "you'd better" in English.