Here is a pretty good list of what you need for a sw tank:
http://www.fishlore.com/SaltwaterAquariumSetup.htm
You can use the same tank and filter, though you will need to clean both thoroughly first. You will need to cycle from scratch. The water itself does not house the bacteria that you grow during a cycle, so sharing water will not help. Probably would not be a good idea to put "used" freshwater into a saltwater tank anyway. As to cost, the short answer is yes...sw setups are generally going to be more expensive than freshwater. Frequently A LOT more expensive. Look at that list of needs from the link above. The 2 items from that list that will really cost you are the protein
skimmer and the
live rock. The fish themselves will also tend to be more expensive than freshwater.