The world faces several issues of energy crisis and environmental deterioration due to over-dependence on single source of which is fossil fuel. Though, fuel is needed as ingredients for industrial development and growth of any country, however the fossil fuel which is a major source of energy for this purpose has always been terrifying thus the need for alternative and renewable energy sources. The search for alternative energy sources resulted into the acceptance of a biofuel as a reliable alternative energy source. This work presents the study of optimization of process of transesterification of vegetable oil to biodiesel using NaOH as catalyst. A $2^4$ factorial design method was employed to investigate the influence of ratio of oil to methanol, temperature, NaOH concentration, and transesterification time on the yield of biodiesel from vegetable oil. Low and high levels of the key factors considered were 4:1 and 6:1 mole ratio, 30 and $60^{circ}C$ temperatures, 0.5 and 1.0 wt% catalyst concentration, and 30 and 60 min reaction time. Results obtained revealed that oil to methanol molar ratio of 6:1, tranesetrification temperature of $60^{circ}C$, catalyst concentration of 1.0wt % and reaction time of 30 min are the best operating conditions for the optimum yield of biofuel from vegetable oil, with optimum yield of 95.8%. Results obtained on the characterizzation of the produced biodiesel indicate that the specific gravity, cloud point, flash point, sulphur content, viscosity, diesel index, centane number, acid value, free glycerine, total glycerine and total recovery are 0.8899, 4, 13, 0.0087%, 4.83, 25, 54.6. 0.228mgKOH/g, 0.018, 0.23% and 96% respectively. Results also indicate that the qualities of the biodiesel tested for are in conformity with the set standard. A model equation was developed based on the results obtained using a statistical tool. Analysis of variance (ANOVA) of data shows that mole ratio of ground nut oil to methanol and transesterification time have the most pronounced effect on the biodiesel yield with contributions of 55.06% and 9.22% respectively. It can be inferred from the results various conducted that vegetable oil locally produced from groundnut oil can be utilized as a feedstock for biodiesel production.