Hi Carl,
Once your PC wants to talk to some other PC in LAN it just sends a broadcast for that mac address and if second PC in on same VLAN it will reply with its mac address.
Now that mac address will be a destination mac address in your frame. Once that frame gets into the switch it will check the mac address table which maintains the entry for mac address plus port number and vlan numer and it will come to know which port the frame should move out to reach the destination mac address.
If that destination mac address is not present in the mac table then that frame will be broadcasted in same vlan and will reach the destination port also but subsequest frames will not be broadcast because after first broadcast the destination mac entry will be learned on some port.
HTH, if yes please rate the post.
Ankur