Perhaps the most common use. As a social formula when you meet people.
Piacere. (sono) Carlo.
Piacere. (sono) Cristina.
Pleased to meet you. Carlo.
Pleased to meet you. Cristina.
This is derived from the original meaning of piacere as a noun, "pleasure." It is a pleasure to meet you. This is why some fancy-pants will sometimes answer, "il piacere e' mio," the pleasure is mine.
The noun in its primary meaning does in fact mean "pleasure."
Il cibo e il vino sono grandi piaceri della vita.
Food and wine are great pleasures in life.
Gli edonisti pensano che il piacere sia la cosa piu' importante della vita.
Hedonists think pleasure is the most important thing in life.
But piacere as a noun can also mean "favor," and is a synonym of favore.
Mi fai un piacere?
Mi fai un favore?
Will you do me a favor?
For this reason, per piacere and per favore as social formulas mean "please."
Mi apre la porta, per piacere?
Potete fare silenzio, per favore?
Can you open the door, please?
Can you be quiet, please?
Literally, when you are saying "please" in Italian, you are asking for a favor: "for a favor."
The idiomatic phrase fammi il piacere can also mean "give me a break" that is, it expresses impatience or disbelief with something someone has said or done.
Sono piu' intelligente di Einstein.
Ma fammi il piacere!
I'm more intelligent than Einstein.
Give me a break!
Now. Piacere as a verb. It gets more complicated.
Piacere as a verb does not mean "to like," but "to be liked." Therefore, with a certain mental contortion for English speakers, you will have to use the indirect object construction to mean "to like." In other words, you will have to say "x is liked by me." This should be familiar to speakers of French and Spanish.
Mi piace la pizza.
I like pizza. (literally, pizza is liked by me)
Mi piacciono gli spaghetti.
I like spaghetti. (the plural of the verb agrees with spaghetti, which is plural, because spaghetti is the subject)
Non mi piaccio con questo vestito.
I don't like myself in this dress. (NOT an indirect construction, a reflexive verb)
Carlo non piace a Lucia.
Lucia doesn't like Carlo. (literally, "Carlo is not liked by Lucia.")
Lucia non piace a Carlo.
Carlo doesn't like Lucia.
