One of the drawbacks of synthetic, as opposed to human hair, wigs is that they can be difficult to style. Fortunately, while hair irons may be a no-go for styling synthetic wigs, you can get great results by submerging your wig in a container of boiling water.
This video tutorial demonstrates one of the many, many different ways to use boiling water to style synthetic hair. There are a lot of different types of synthetic wigs/extensions out there. Styling it this way is mainly for non-heat resistant hair, or synthetic fibers that are mixed with human hair. But you can still use it for high-heat resistant, and human-hair pieces too!!
As is mentioned in the video, if you aren't doing this for a wig and are just using this for extensions or a hair piece, you can just put a cup of water in the microwave until it's nice and hot. Once the water is hot enough dip the hair in the cup for a few seconds, and follow the same steps for drying/styling.
How long you leave the cup in your microwave depends on the microwave itself, but 5 minutes usually works. If it isn't hot enough just pop it back in there for a little longer.