You have a very well made revolver that has a bit of history to it. Durable, accurate and reliable.
Some info for you- http://en.wikipedia.org/wiki/Smith_%26_Wesson_Model_15
To read the model number, open the cylinder. Model number would be stamped on the frame, covered up by the cylinder crane when cylinder is closed.
Your revolver is nickel plated. This was done as a protection from corrosion (pre-stainless steel). Do NOT use a highly abrasive cleaner of any type, or you will abrade your way thru the electroplating. There are polishes intended for use on nickel- check with a good silver shop. Myself, I use a product called Flitz, soft cloth, hand polish only- no power tools.