Techniques for propagating plants vary greatly depending on the plant itself and the purpose. Commercial propagation techniques do not actually vary that greatly from those used by the home gardener, it come down to a matter of scale.
Plant Propagation Techniques
Three main techniques are used for propagating plants
This includes cuttings, division, layering, grafting and budding. Four main types of cuttings are used in propagation techniques hardwood, softwood, semi hardwood and herbaceous. These simply refer to the age of the material taken to make the cuttings, except for the herbaceous type which are cuttings taken from plants such as dahlias and carnations, one of the easiest forms of propagation in many respects. Some of the easiest cuttings are from succulents such as crassula propagation.
Simple germination techniques include direct seed planting others include soaking, stratification and scarification
This is a way of actually 'cloning' plants' in a sterile laboratory situation
It need to be emphasized that different plants require different techniques and not all methods are easily transferable to other plants. Even the scientific approach of tissue culture have not been perfected for all species, many being rather recalcitrant to respond to this method.
An excellent reference for detailed explanations of methods is - Hartman & Kester's Plant Propagation: Principles and Practices