Electroplating is the deposition of metal ions from solution onto an electrically charged surface. The surface must therefore be conductive. Plastic is not conductive, so direct electroplating of plastic is not practicable. Instead, the process is performed in steps, covering the plastic in an adhesive conductor, like metallic paint, before performing genuine electroplating.
There are two methods to plate plastic: One is to roughen the surface to allow metal to adhere. Then electroplate over that layer to build up layers of metal. This process is called electroless, autocatalytic or chemical plating.
The second method is to apply conductive paint to the plastic, then electroplate it.
To begin the roughening method, first clean the plastic part of all oil, grease and other foreign matter. This process can be made complicated if you want to be thorough, with a long series of applications of acids and bases. Rinse with water several times after each step to clear away the prior cleaning agent before the next is applied.
Drop the part in a chrome-sulphur bath. The acid will pit, or etch, the surface, so that metal can adhere. An alternative method of etching is to sandblast the surface.
Drop the part in a palladium chloride bath. This will leave an initial layer of metal which will allow electroplating the standard way. Specifically, the part will then be electroplated with copper as yet another preparation layer, then gold, chrome, nickel or whatever the final metal layer is to be.
Purchase conductive paint. Inexpensive conductive paint can be purchased from Acheson Colloids or Cybershield.
Clean the surface, as above.
Apply the paint.
Electroplate with an initial copper layer, as above. The rest of the electroplating is the same as in the pitting approach.
"Standards for Electroplated Plastic" is the standard handbook for electroplating plastic (see Resources). If you want a chrome finish, consider vacuum metallising instead. It is the process used on mylar balloons. Chrome should be reserved for objects that will be subjected to water exposure and wear and tear.
Do not electroplate with chrome in your home; its toxicity requires special handling. Numerous warnings of how electroless plating of plastic can go wrong can be found at finishing.com (see third Reference below).