Your question is quite general and explaining the methods of CEA here is beyond the scope of a brief answer in RG. Several (also open-access) sources are available in the web, for example "WHO Guide to cost-effectiveness analysis".
I do not know whether it was your intention but when it comes to difference between societal and health system perspective:
Societal perspective includes benefits gained and costs borne by the whole society, including non-health sector entities e.g. households, employers, government. Health system perspectives only accounts for benefits and costs in health system.
This question is core to health economics and needs a tectbook for a comprehensive answer. Having worked in this field for several years, a shortcut would be to look at the information on DALY and QALY - both indicators are readily calculated for most health interventions and provide the answer to your core question.
I just echo previous commentators on the broadness of your question and the availability of materials/texts on it. CEA studies are vastly helped by the Global Burden of Disease studies which you can use for DALYs.
It is certainly a broad question. You would need a good textbook. In order to get started with all the topics related to the economic evaluation of health technology, I would suggest m. Drummond et al. Methods for the economic evaluation of health care programmes, last edition. You will find the tools you need for your project. Once you get to know how to perform an economic evaluation, there are lots of academic journal publishing paper on this topic (e.g., Value in Health, Pharmacoeconomics,...).
I agree with all the comments. By way of short cut I wish to make my contribution which is not an end and a substitute for the need to read extensively.
From the meaning of perspective which implies view point being considered in economic evaluation or vantage position of consideration, CEA methodology from the various perspectives including societal perspective and health system perspective are the same. The only difference is the various costs to be included in the analysis.
In societal perspective, all costs all considered regardless of who is responsible. In the other perspective such as health system not all the costs are considered 'relevant' to the researcher or contracting agency.
For example costs such as transportation, indirect cost resulting from loss productivity, hotel cost of care givers in addition to drug, diagnostic/monitoring tests, consultation, admission etc are considered in societal perspective. The reason being that the cost of transportation of the patient is not available to pay for other expenses.
For the health system, since economic evaluation/pharmacoeconomic is for decision making, some of those costs listed above such as transportation, hotel cost and indirect cost are not relevant in the various decisions to made in the health system. Hence they are not considered.
Closely related is third party payer who also would include any cost that is relevant to his decision.
In summary, it is broadness and the various cost of inclusion that differentiate the various perspective.
For the actual calculation, the Cost Effectiveness (CEA) Ratio would have to be computed. The cost here implies all applicable cost components relevant to the perspective of analysis as earlier explained. The Effectiveness which is usually measured in natural units could be surrogate (intermediate-e.g. mmHg of BP dropped in hypertension after an intervention) or other outcomes such as lives saved. QALY can also be used as in Cost Utility Analysis which is considered to CEA to which patient perspective has been added. We also have Incremental Cost Effectiveness Ratio (ICER) where the therapeutic option with greater cost has superior clinical effects.
Cost-effectiveness analysis can be seen as a way to examine both the costs and health outcomes of an intervention to society or the health system. It tries to do a comparison between an intervention and another intervention (or the status quo) by estimating how much the gain of a unit of a health outcome can cost