"Simulation" can refer to more than one process of estimating the behavior of a system or quantities that can be compared to measurement.
It may be helpful to choose a type of process you are interested in and develop a physics based simulation of it.
Keep in mind that a numerical method is not necessary for building a simulation and that computers are not necessary for numerical estimates. Hence, there are at least three distinct disciplines being discussed.
As an example, projectiles (baseballs, munitions, missiles) can be "modeled" using results straight from a high school book: x-x0 = vx0*t, y-y0 = vy0*t - 0.5*|g|*t^2. One does not need a computer, maybe a calculator if your arithmetic is rusty, to evaluate quantities based on this system of equations. The real issue for the modeler is "does this model accurately represent the system to which it is applied", "can I trust the estimates"?
You might be surprised at just how much can be squeezed from known exact solutions when they are applied thoughtfully.
If you are interested in modeling a complex system then you will eventually need to delve into classic numerical methods, Numerical Recipes in FORTRAN or C is a good place to start but that recipe book will not teach the art of modeling and simulation. You will need to test out those algorithms and learn which make sense to use for a particular problem. Many of those recipes for solving ordinary diff eq and partial diff eq are not stable or convergent (and they point that out) so you'll need to dig deeper.
The nature of your simulation approach may depend on the type of problem you want to solve, or on your available resources. There exist multiple techniques for solving the same set of equations, or types of equations. So you have a lot of freedom and that can get confusing.
Going back to the projectile problem if you add air resistance to the problem for high speed objects you may not get an exact solution and need numerical methods to approximate a solution. Now a computer will be a useful tool. BUT you will need a "model" of the air resistance (drag) force, and possibly lift. While the coefficients may be a function of knowable quantities you will likely want to keep this constant for simplicity (especially if you are just learning). The need for this now introduces an entirely new task for the modeler. The aero forces may be known, measured, capable of being estimated by a simple model, or you may want to get spun up to build a detailed simulation that couples fluid dynamics to the projectile motion so you can see buffeting and turbulent effect arise. That would be "hard". To the point made in the other answer, we usually start by:
1) identifying what we want to model then,
2) decide whether we can use know equations or solution, or need to solve the equations of physics, or can build up a statistical model,
3) along the way we decide what to neglect (and hopefully justify that),
4) then pick an approximation method (numerical, mode expansion, etc)
5) if needed write software to perform these calculations (for accuracy and speed)
Steps 4 and 5 will lead down a long path into completely independent disciplines.
If you just want to learn how physics is modeled using these techniques you'll need to look at physics books that have a modeling or numerics section. I believe that newer editions of Fowles Mechanics is expanded to include some numerical sections. There is also "Modeling and Simulation of Aerospace Vehicle Dynamics" by Zipfel, "Method of Moments in Electrodynamics" by Gibson, etc. The problem is that most basic physics texts do NOT contain modeling and simulation sections, and most modeling and simulation books are either (1) too general and don't show applications, or (2) are too specific and don't explain the numerics adequately.
You state that you are a "beginner" but not whether you have a deep understanding of physics and not numerics or if you are a beginner at both. This would help w/r to a recommendation.
Last but not least different phenomena will require different techniques.
Rigid body motion -- Forward propagating ODE solvers (like Runge Kutta, etc)
EM and acoustic Scattering -- Boundary element methods
Solving the wave equation in refractive media -- Finite difference, or Finite element method
This doesn't even touch upon perturbation methods, etc.
and so on...
So I'd recommend starting with something like projectile motion with air resistance. This will point you in the direction of ODE solvers which are fairly easy to code and test. For linear resistance you have an exact solution to Newton's equation of motion so you can check your result. Then you can add Earth rotation effects etc making your model more realistic and learn more in the process.