(a) Different methods used in Vegetative Propagation are:
(i) Use of modified underground sterns e.g. cocoyam, corn, sucker, etc.
(ii) Cutting of stem with two or three nodes and buds, e.g. cassava, croton, hibiscus, Ixora (sweet potato)
(iii) Flesh leaves e.g. onion, Bryophyllum/ bubuks
(iv) Budding: a dormant bud from one plant/ scion, e.g., citrus, mango.
(v) Grafting, where part of one plant is joined to another of the same or related species, e.g., citrus,mango.
(vi) Layering: A branch close to the soil is bent so that part of the branch touches the soil. The end of the branch is then tied to a firm support. A ring of bark has to be removed from the part of the branch touching the soil while a slit is made half way through the branch. Then this part has to be pushed below the soil and cover with soil while a heavy object is placed on the heap of the soil to weigh it down, e.g., Bougainvillea, Rose plant (sp) cocoa, coffee.
(vii) Marcoting, e.g. mango, lemon (citrus), Rose (Rosa sp)
(b)(i) Advantages of Vegetative propagation are:

young plant uses food reserves of the parent as it becomes established or easily established.
Growth in young plant is rapid since there is no resting or lag period
Only one parent is needed
desirable characters are retained
offspring is identical to parent
offspring matures more rapidly
are less susceptible to adverse weather conditions
plants that do not produce seeds can only be [propagated vegetatively)

(ii) Disadvantages of vegetative propagation are:

No new varieties are produced; no mixing of characters
offspring and parents compete for light and nutrients since many individuals occupy a limited area of land
overcrowding; reduces resistance to disease
reduces resistance to changes in climate / adaptation to environment.
colonisation of new localities unlikely, since offspring is always produced close to parent plant
diseases of parents will be transmitted to offspring
undesirable features are easily transmitted to offspring.