I would like to add to this. A network tap will sit in-line and monitors all traffic passing in/out of your switch. However, it will need to sit between the switch and the router. If you don't have a simple port to port connection this becomes more difficult.
If you can, like suggested above, configure your switch to mirror all traffic to a monitor port then you can monitor all traffic on the switch that way. However, I believe there will be some data loss if the traffic becomes too much for the switch to handle (check your switch specifications for specifics).
Either way, you will need some software/hardware to view the traffic. I work for a company that develops NetScope, which works like a tap interface and sits in-line on your network. It will also monitor a mirror port on a switch.
There are some free programs out there that will do it. Some a Linux-based ones based on ntop.