Most ethernet cards that can do 100 have a LED that comes on if it IS doing 100, in similar fashion most switches have LEDs that light or change color if the port is 100.
Software is trickier, the Unix I use has ndd commands but you need to know the interface name. Macs use Apple System Profiler speed and duplex are in the Network Overview. In Windows before 2000, the ethernet control panel is written by the card vendor, and so different for every ethernet card model. There is no general rule that one can give.
Via a protocol called N-way, copper based ethernet set to auto negotiate chooses the fastest speed and duplex both cards can do. You VERY rarely wish to override this. (some Cisco switches are very poor at N-Way and need help, converting copper to fiber also needs manual settings) The major limitation of N-Way is once you, the human, disable it anywhere on a wire, you must have control of each end of that wire.
Switch End Computer End
Auto Auto Works
Auto Full Fails
Auto Half Works
Full Auto Fails
Full Full Works
Full Half Fails but may appear to Work
Half Auto Works
Half Full Fails but may appear to Work
Half Half Works
As you can see leaving it auto is best (since N-way only checks the cards, it sometime is confused by poor wire)
I tried to remain child-like, all I acheived was childish.