Tips for Zermatt?

Well fate has placed me in Zurich for a bit so of course I brought the skis and I've booked a week in Zermatt. Never been to Switzerland before, the only place I've skied in Europe before is Mayrhofen and the Hintertux in Austria. Any tips? Favorite runs? The lift tickets are confusing me because I'm not sure how the different areas work. Also I brought my huge New Life's because fuck it, was that silly? I know Europe has a strange obsession with grooming everything but they seem to have gotten like 2 feet in the last couple days if I'm reading the reports right. Powder stashes?