I guess the most read book is "Methods for the Economic Evaluation of Health Care Programmes" from Michael Drummond et al. (2005). Also, I find the Oxford Series "Handbooks in Health Economic Evaluation" pretty useful.
Please see if this WHO manual is helpful for your purposes (though it is specific for cost-effectiveness analysis). However, as said before, Drummond's textbook is a must read for those deeply interested in health economics.
I have experience using TreeAge software, that is used for construction of decision trees and Markov modeling and other robust analyses. It is a paid software and demands previous training.
If you are interested in some basic calculations this website may be useful: http://www.healthstrategy.com/objectiv.htm
One of the first critical analyses of cost-analysis of RCTs was a paper by Adams ME, McCall NT, Gray DT, Orza MJ, Chalmers TC, "Economic analysis in randomized control trials" Medical Care. 1992 Mar;30(3):231-43. Although Scholz has already suggested a more recent, and undoubtedly much more complete, book, I believe that the paper, which is easily accessible, and I'm attaching, has useful information about desirable characteristics of an economic analysis of an RCT.
As I don't know your bacground I would recommend a book "Health Economics for Non-Economists: An Introduction to the Concepts, Methods and Pitfalls of Health Economic Evaluation" by Lieven Annemans. Ease to read and understand. Unfortunately it is not for free...
From a public health perspective, I have found this briefing paper "Economic appraisal of public health interventions" by UK NHS Health Development Agency quite interesting (Kelly et al., 2005)
sorry for the late reply! Concerning the software, I would say you can use anything from Excel to R (or any other statistical software). If you want to build a model you could also use TreeAge, but is not for free.
Here is an open course from JHSPH with a comprehensive reading list if your goal is to be able to read and understand cost effectiveness in publications: