This question is a little too open-ended to provide a clear answer. Stated preference conjoint analysis includes a number of different methods, and the most appropriate one will depend on what you're trying to do. Do you just want to know how sensitive the decision to purchase is to price? Then simple binary choice would probably suffice. Do you want to be able to simulate market shares given different prices? Then a discrete choice experiment might be better. Do you want to know how sensitive the quantity purchased is to price? Then you probably need some form of full-profile rating or constant-sum allocation. You have to decide what question you're trying to answer before you can decide on a method, and how you conduct the analysis will depend on the elicitation method you used. Binary and discrete choices can be analyzed using conditional or multinomial logit, and full profile and constant-sum tasks can be analyzed using a simple linear model, or more complex models such as tobit, poisson or negative binomial. Obviously all of these can be conducted in R. See this post for some options for analyzing discrete choice responses... Conjoint Packages for R
Finally, stated preferences might not even be the right way to go. If you're looking to estimate the price elasticity of demand for existing products, a revealed preferences approach, where you analyze actual consumer behaviour, would be more appropriate.