Basically there are three - Melt & Pour, Cold Process and Hot Process. A prepared or pre-existing melt and pour base is usually acquired first although you can make this base too. The name says what it does - you melt the soap pieces add a fragrance and colour, pour it into a mould and it is ready to use when it has hardened. This is because the curing has already occurred when the base was made. This is the easiest and quickest method to have soap with a fragrance and characteristics of your choice. However, many bases contain sodium laureth sulfates and most will not be organic or all natural due to its ability to melt and pour. It is important to check the list of ingredients before buying.
Cold process is a method where fats and oils are converted to soap without cooking although both the oils used and the lye/water solution are heated to a desired temperature before combining. The mix uses its own heat generated by the combining of the two solutions to start the saponification process where soap molecules are created. The soap mix goes through a heated gel stage once placed in the moulds, cools and then hardens. A curing time of 4-6 weeks is generally allowed in order for the lye to be completely converted and worked out of the batch and the water to evaporate. This soap contains the natural emollient of glycerine. This method appears to be the most popular method.
Hot process is really "cooked" soap where the oils and lye/water mix are boiled until most of the water has evaporated and the soap quickly solidifies on cooling. It goes through the gel stage before being placed in a mould. Some say the soap requires no curing time but we believe the saponification process has not fully completed for at least a few days or a week after 'cooking'. Fragrance and colours are added towards the end of the cooking but due to the higher heat temperature this can be problematic with essential or fragrance oil properties.