Cold Process Method
Cold process soap is known for its hard, long lasting quality. Depending on the oils used, the bar can have great lather (coconut oil has awesome lathering properties), be incredibly mild (olive oil is renowned for its gentle qualities) or be very moisturizing (with the addition of oils, such as shea and cocoa butter or hemp oil).
Melt and Pour Method (great for kids to do)
This is glycerin soap, or clear soap. It can be very nourishing and moisturizing. Glycerin is a “humectant,” so it draws moisture to itself. The theory being that if you wash with glycerin soap, a thin layer of glycerin will remain, drawing moisture to your skin.
Hot Process Method
A newer trend in soap making, with this method, you can make the soap in the morning and use it that very night. It's basically like the CP method, where you combing the oils, water, and lye, except you make the soap on your stove top. Very cool. I haven't tried this method, but it seems relatively easy and convenient.
This method is often used to preserve the scent or the healing properties of some essential oils. You take your CP soap, grate it up, heat it up in a kettle over your stove top, and the mixture melts into a wonderful mushy mess.