How do you packet sniff a network that uses a cisco router or switch and want to see all out/inbound traffic?

Im just curious how it is possible to see all outbound and inbound traffic on a large network. I'm apart of an IS team, and was just curious what you would do. I know you need to have windows to say, install wireshark, but on a switched network, or a network with a router, how would you see ALL inbound and outbound traffic? Can wireshark be installed on the actual router, or would you have windows pc that connects to the router console, and then sniff from that. How does this work? I mean, I can snigg my local traffic on my hub, but what about all other traffic? I am curious to see who is using bit torrent and such programs, and just get an idea of overall traffic that comes into our network, and leaves our network. I'm obviously a newbie, but my manager says for me to experiment as much as possible. We have a very liberal IS environment, being that we are a non-profit facilitiy. So, any help would be appreciated!. I just always wondered how that it was possible to packet yze route