Modeling is useful when multiple actors are interdependent over time such that macro, or collective, outcomes of micro interactions are hard to grasp by the unaided reason. Math is best for its clarity and explicitness: if someone claims to have a result you only have to verify the proof and its assumptions. When analytic solutions or elegant proofs are not possible, simulation models can be made, which however are much harder to verify, in particular if there are many lines of code. Yet often there is no other option.
A fundamental paper:
One of the best motivations for modeling:
On agent based modeling (ABM):
You don't have to be a mathematician or a computer scientist to use math or simulation models. To develop basic skills, an excellent short book is:
The title is too modest; it is a primer for any kind of mathematics in all kinds of empirical sciences.
You might continue the former primer with this still very good old textbook:
Introductory notes on differential equations by Robert Terrell are freely accessible on the Web. Among basic skills also belongs programming. Making simulation models and numerically solving (systems of) differential equations is nowadays done by many in the Python language; see its Scipy package for math, and this guide for proper Python style. If you're used to SPSS, Excel or Stata, the Pandas package smoothens the transition. Watch out for old Python 2 code, which is abundant on the Web and in text books, but will no longer be maintained. Translate automatically all your Python 2 files to Python 3, with the 2to3 command in Linux (which you should have anyway). If you want a single language for all your social science work, however, R is best (and the deSolve packages makes it possible to solve differential equations, too).
Evolutionary game theory
People's decisions and fates are interdependent, which is formalized in game theory. To sidestep the ludicrous assumption of perfect rationality, you can resort to evolutionary game theory. With apologies to John Maynard Smith for not recommending his classic textbook, I suggest:
Early 21st century statistical physicists have become the most prolific producers of models of social phenomena (and mathematicians, computer scientists, biologists, and engineers along with them). An introduction without math:
See also social networks on this website.
Large computation jobs beyond the abilities of a PC can be done on the computers of the University of Amsterdam (SARA).
An aesthetically mouth-watering case study of a mathematical approach to cultural phenomena is: