I tried to search for this problem but I don't know what exactly I'm looking for.
I found some empirical parameters that correlate but not linearly. An example follows: $Y_1$ and $Y_2$ are the values that I need to calculate in the future, they were found through existing data analysis. $X_1$, $X_2$, $X_3$ and $X_4$ are the parameters that correlate with $Y_1$ and $Y_2$. I would like to create an equation that correlating these data in an approximate way: $f(X_1,X_2,X_3,X_4) = (Y_1,Y_2)$
I'm a programmer, not a mathematician, so please respond in a way that I can understand.
It seems like you are looking for regression or fitting of a data set to a function. (If you don't care about knowing $f$ analytically, look up machine learning). Hopefully I am understanding you correctly.
Usually, for numerical fitting, you pick a form for $f(X)$ and then computationally fit to it. For instance, in Python, you could fit a polynomial to it or some generalized linear model. For general non-linear fitting (e.g. by Levenberg-Marquardt), one can fit a function to the data by non-linear optimization, usually by least-squares error minimization (e.g. in Java). Basically the parameters of $f$ are chosen to be as close to the observed $Y$ given $X$.
Then again, if you really want to compute non-linear correlations, I'd suggest looking at rank correlations, for example.