I am trained as an epidemiologist. Early in my career, statistical models were a black box, and when in doubt I was advised to go see a statistician. This never sat well with me, so I became interested in statistical modelling and since have put in time learning statistics and probability theory. I am now able to learn, understand, and apply statistical methods that are new to me, but for the first time I have found a model that will likely help with a problem I am dealing with, but as far as I can tell there is no existing software to estimate the parameters of this model. This entire area of statistical modelling is actually a complete mystery to me, and I'd like it not to be.
So...which resources are the most appropriate first step for a novice who wants to learn how to write their own programs for estimating statistical models?