Quick answer
me suena
Natural: it rings a bell / that sounds familiar
Literal: “it sounds to me”
How it is used
Ese nombre me suena.That name rings a bell.
Me suena su cara.His face looks familiar.
No me suena de nada.It doesn’t ring a bell at all.
Me suena haberlo leído.I have a vague feeling I read it.
Where it is said
Standard everywhere, though it is heard most in Spain. In Mexico <b>se me hace conocido</b> covers the same idea.
A mini dialogue
— ¿Conoces a Pablo Ramos?— Do you know Pablo Ramos?
— Me suena, pero no sé de qué.— It rings a bell, but I can’t place him.
Watch out
me suena
The thing remembered is the subject, so the verb agrees with it: me suenan esos nombres, not me sueno esos nombres.
me suena
Sonar here is nothing to do with soñar (“to dream”); the tilde changes the word completely.
Check yourself
What does “Ese nombre me suena” mean?