Unlike everyone else who seems to be annoyed at those that didn't see the first series (or played the games, etc., etc.), I was not aware of what I was picking up. My friend recommended me this series and I did not see the first series available, so naturally I picked this up.
So coming from the perspective of someone who hasn't seen the first series, it was still relatively easy to pick up. I had to fill in some blanks and make a lot of assumptions, but it also forced me to watch more to help me understand what was going on.
Regardless of all that, even if you haven't watched the first series or played the games, it's still a very enjoyable series.
...however I'd probably go back and watch the Higurashi No Naku Koro Ni first.