Can i interface an ethernet card with a microcontroller and connect the microcontroller to communicate via net?

my objective is to make microcontroller based communicatiion device that can communicate with a pc or similar device through internet (ethernet). it communicates through a traditional lan card on isa or pci bus. so is it posibble to connect our device to the internet provided by our internet provider i mean whether we have to take its permission or can use the IP of the existing cable net for its connection to the internet? also tell if using the same IP is possible then continue using the internet using our pc and device simultaneously or one at a time having same IP address?