For piping you'll need:

Nothing - The ultimate in laziness, just buy pre-made icing in a tube

Greaseproof paper/Silicone paper/waxed-paper - you can use this to make a simple piping bag. You can either just cut off the tip (start small, you can always cut off more if the hole is too narrow) or use it with a nozzle (piping cone). Baking parchment will normally be too thin, and disintegrate when you apply the piping force.

http://www.ehow.com/how_2150375_piping-bag.html

Piping device - good for kids/those that find piping bags too difficult. They're a pain to clean, and often leak, and you'll never be able to pipe out all the icing so make sure you have plenty if you use one of these.

Nozzles. little metal cones with various size/shape holes at the end. you'll need round ones for lettering and general piping, the star shaped ones are good for buttercream, and tear-drop shaped ones for piping flowers.

When you get to the actual piping, you might be piping straight onto the cake, or making icing shapes for later assembly. When creating shapes for assembly, you'll need more greaseproof/Silicone/waxed paper. You could also use a non-stick mat. The advantage of using the paper is you can print out or draw the design you're piping and place it below the greaseproof, then simply trace the shape with your icing bag.