I am trying to understand rugby and I get really frustrated not knowing what the penalties are for. What are the penalties in rugby and how are they called?

You mean what are the different things you can get in trouble for? There are lots of things. Most cases its passing the ball forward which is a huge no-no. Also high tackles, which is tackling above the shoulders. There is also picking up the ball before its out of the scrum or the ruk. In all these cases you usually do a scrum to fight for the ball on the penalty.

URL has "Rugby Penalties Explained"