These three verbs in Spanish induce to confusions since in other languages is used a same verb for the three meanings. In this article we are going to explain the meaning differences that there are between these verbs.

To know something or somebody means that we have had some experience of the thing (or person) known.It is possible to know: a book, a film, a place, a person. The use of the preposition a is obligatory when the Direct Object is a person:
Vamos a tomar algo. Yo conozco un sitio por aquí donde ponen una tapas buenísimas.
¿Conoces a Fernando? Es un chico muy simpático.

1.- It is used to speak about learned abilities, as for exemple: to swim, to draw, to speak a language...
¿Sabes hablar chino?

2.- It is also used to speak of the knowledge that somebody has of an information.
¿Sabes que María se ha casado? / ¿Sabes quién viene esta tarde?

1.- It means the possibility or capacity to do something:
Yo sé tocar el piano, pero hoy no puedo tocar nada porque me duele mucho la cabeza.

2.- It is also used with an infinitive verb to ask permission or to issue orders and instructions:
¿Puedo sentarme aquí?

Some times poder and conocer are used in the same cases, and then they are synonymous:

1.- When conocer means to find out or to be found out of an event or a new.
Conozco / Sé las dificultades de este trabajo
Hoy las noticias se conocen / se saben al momento en cualquier parte del mundo

2.- When we want to express our knowledge or ideas about a subject or science:
Ramón conoce / sabe muy bien su oficio
¿Conoces / Sabes la teoría de la relatividad?