There are a couple of different kinds of water-soluble stabilizer. One is clear and plastic, and that brand is Sulky Ultra Solvy. The other is soft and fibrous, called Vilene. Both work well. Vilene is used in this demonstration.
Use a size 11 or 75/11 sharp sewing needle. A sharp sewing needle has a smaller, finer point than an embroidery needle. That means it will make smaller holes in the stabilizer.