usi mi fa piacere prevalentemente quando il piacere deriva da qualcosa che fa qualcun altro e si riflette su te. ad esemio " mi fa piacere che siate venuti a trovarmi" "mi fa piacere che tu abbia superato l'esame". nel primo caso provi soddisfazione per una cosa che si riflette su te, la seconda si riflette su altri ma ti unisci al piacere provato da altri
for those of you who wonder. piacere = please (as in pleasure) mi piace (literally= it pleases me) = I like... ti/le piace = you like... gli piace= he likes... le piace = she likes... ci piace = we like... vi piace = y'all like.. gli piace = they like...
in this case we use 'Indirect Object Pronouns' (to answer the question 'to whom' or 'to what'), to whom it would be pleasurable (literally)? to her ! le piace la pasta!
One small problem with that. Piacere is also a noun, meaning pleasure, and that's what it is here in mi fa piacere, also in the common polite greeting Piacere!.
As one doesn't "do pleasure" or "make pleasure" in English (;-) the closest translation is probably "it makes me pleased". Duo accepts this (though not many of us would say it) as well as the much more frequent "I'm pleased".
Glad is closer to each of contento, lieto & felice than to piaciuto, but "I'm glad" is a sensible idiomatic translation here.
But it apparently is an idiom, with a meaning reserved to "it makes me happy/glad" = "I'm glad/happy". You'd probably have to use something else to say "She/he makes me happy", like "Lei/lui mi fa piacere".
PS I entered "She makes me happy" and got it wrong, of course. Google translate says that lei mi fa piacere means "she pleases me" - which would be distinct from the other idiom, "lei mi piace" = "I like her", even though it literally means "she pleases me".
To say "it's my pleasure" as a way to say "nice to meet you" you'd just say "piacere" that's the expression you use to be polite when someone you met. But "mi fa piacere" is used to say that something (not mentioned here) gives you pleasure or makes you glad like "mi fa piacere vederti" or "mi fa piacere studiare italiano"
According to ReversoContext that is OK. Click on the button for "I am delighted" to see examples of this usage: http://context.reverso.net/traduction/italien-anglais/mi+fa+piacere