There are two broad types of plastic: thermoplastic and thermoset. Thermoset cannot be melted once it has been formed, making it difficult or impossible to reuse. Luckily, around 80% of all plastic is thermoplastic - meaning it can be remelted and recycled into a new product.
Plastic products often have a triangular logo on them that describes the material they are made from: the triangle will contain a number that can be used to identify the general type of plastic.
The easiest way to identify the type of plastic is to use the recycling logo, described above, however not all products will contain this. Other methods of identification include whether a product floats or not, the sound (if any) it makes when deformed and the characteristics of it burning (not recommended!).
For more information on plastics and recycling them, visit Precious Plastics.