Models can be empirically found, or derived from fundamental laws. A good model has a well-defined domain of validity, in which it leads to unambiguous, self-consistent results. Ideally it is easy to evaluate. To adaption of a model to a specific problem instance is done by model parameters, which can be defined/measured independently or left as free parameters to fit the model to a realistic situation. A large number of free parameters makes it difficult to assess the validity of the model without independent knowledge.
You can also make a model simply by fiddling around with the data, as NASA did when studying the erosion of O-rings used in the space shuttle:
- A mathematical model was made to calculate erosion. This was a model based not on physical understanding but on empirical curve fitting.
- Wile, Dr. Jay L. Exploring Creation With Biology. Apologia Educational Ministries, Inc. 1998
- Feynman's Appendix to the Rogers Commission Report on the Space Shuttle Challenger Accident