To get phone in silent mode touch where it shows none,it will show if you want it set for indefinite, or how many hours .
The same goes for priority,it will ask for indefinite or how many hours you want it set for.
So you dont use the volume slider to set it to silent you touch none and then set it for indefinite or how many hours you want it silent.If you use the volume slider and move it all the way to the left it will be in vibrate mode.
A box pops open when you touch none with the options just mentioned.
Edit:
None: your phone is silent for rings/messaging
Priority :means your contacts rings or /messaging sounds will still be heard .I think for all contacts (it might just be for favorites I forgot for sure lol )
All: Rings /messaging as normal