One of the most important things you can do with this bike is take it to a local bike shop and have it checked out. I've read some real horror stories from owners of department store bike. A good bike shop can make sure it shifts correctly and that everything is tight and well lubed. If your just riding it around town this bike should be just fine for you. I wouldn't recommend taking it off road on any trails though. You might find yourself walking home. Also the folks at the bike shop can give you some riding tips and maybe adjust the bike to fit you better, making it more comfortable to ride.
On the shifting question, definetly try to plan you shifts. If you see a hill coming, shift down before you have to start pedaling hard. The worst thing you can do is shift while pedaling hard. This can cause the chain to bind and break and that's not a good thing . If you do find yourself on a hill and need to shift down, try giving the bike a couple of hard pedals so you can pedal easily for a couple of revolutions while shifting down. You will get better at all of this after you've been riding a while.
Have fun on your new bike. I absolutely love riding mine.