Richard F. just answered a question about how they make gas, so he's our scientist to answer this question as well.

At an oil refinery, lots of other substances are collected besides oil and gasoline. Some of these substances can be combined in a chemical factory to make various kinds of plastic.

There are many different kinds of plastic. Some are clear, but some have other materials put in them to colour them. Some are made into threads to make cloth, rope or fishing line. Some are made into sheets to make plastic bags or plastic food wrap. Some are melted and poured into molds to make solid shapes. Some are hard, like the plastic used to make Lego blocks. Some are softer, like the rubber tires on cars. Some are brittle and break easily, and others are stretchy. Some can be made into foam pads or styrofoam and used as insulation. Plastics were only invented about a hundred years ago, but our lives today would be very different without them.

Ben, we also looked in your school library for books about plastic and found this one

Let's visit a toy factory
Miriam Bourne
688.7 bou

In it you'll see how plastic is used to make toys. Thanks for you question.