I highly suggest reading the books. They're about 1,000 pages each (there are 5) but they are awesome. The books explain things in much more detail, which makes watching the HBO show much easier to understand.
I watched season 1 before I read any of the books and was instantly hooked. The "zombie things" at the end were the "white walkers"...You need to go read the first book "The Game of Thrones"
I read all 5 books before Season 2 aired because I couldn't stand not knowing what happened. I don't read many books so for me to read 5... back to back...it's a great series.
ALSO do NOT go to the wikipedia page for "Game of Thrones" if you don't want to see spoilers...it summarizes the entire series there so don't ruin it for yourself if you plan on reading the books!