The reaction is pretty simple and easily done, it could be written with this two simple equation:
2 AgNO3 + Cu = Cu(NO3)2 + 2 Ag
Ag2SO4 + Cu = CuSO4 + 2 Ag
What will you need? Almost nothing. A flask or a container (preferably glass). Four chemicals: silver-nitrate or silver sulfate, some metallic copper and distilled dihydrogen monoxide (:water).
Where to get these from? Silver salts could be bought from the local chemical supplier or somewhere where they sell things for classic photography. Or by dissolving mothers favorite silver earrings or necklace in some nitric acid(:
How is it done? Make a solution (circa 10g/liter or more dilute) of silver nitrate with distilled water, add some silver sulfate in any portion (what won't dissolve), place it in a dark place where it won't be disturbed for a month or so and drop a few pieces copper metal in it. Close the door and do not disturb it for a while.
After a little time the solution will turn blue and small crystals of silver will appear on the surface of the copper (the silver nitrate is well soluble in water and it reacts fast). This will act as the body of the metal tree. From this, to the end of the month, the silver sulfate will act as the source of the silver and since it is not well soluble it will cause a more controlled and much better looking crystallization of the metallic silver on the surface of the copper.
So you have nothing to do, just leave it in the dark (silver salts are highly unstable, and decompose on contact with light) and always remember the golden rule of crystal growth: put it on the shelf and forget about it.