It partly depends on what you want to do with the data you have. If you ask five different people in five different fields you will get twenty five different answers
If you want to pursue this, I suggest starting with the wikipedia article on interpolation (mostly focuses on 2D but the principles extend to 3 or more dimensions).
As a rough overview (which you probably already know) the key is finding a function from known output and input values that allows you to calculate a results where the outputs are unknown.
Finding this function can be performed using a number of different methods which depend principally on the function in question. Some will be performed explicity (plug known numbers into a function and it return parameters) others need to iterate repeatedly until an optimum set of parameters is found. Optimisation and searching are very big fields in themselves! You will find all sorts of variations which depend on the data itself and how reliable it is etc etc. but try not to lose sight of the fact that they are basically trying to do the same thing. (several methods are explained in the numerical recipe book linked above).
The other main facet is where the function is applied - locally to just a few points in a matrix (local areas could be determined using a triangulation method, for example), recalculating the function repeatedly over different points, or globaly over all your points. Naturally you also need to choose the right type of function to represent you data and the expected results.
A google for "scattered interpolation" turned up this file http://www.idiom.com/~zilla/Work/sca...erpolation.pdf
(1.1Mb) which is a survey of scattered interpolation. It is not very good on it's own, I add, as it is a presentation and is obviously aimed at a specific audience and lacking the deatiled explanations of a text book or even web article but I think it gives enough terms for you to follow-up the specific methods.
A word of warning though - if you are not very mathematical (i.e. no university level mathematics, this includes me) some of it will look pretty ugly. Bear with it though, because the concepts are usually pretty straightforward - it is often just a matter of finding the right diagram or description at which point it will often 'click'.