How are laws proven in general? 
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*This may be a bad question, but what are the ways that laws are proven? I would expect that some ways would include by proving them mathematically or through experimentation.

*My biggest question about this is about proof through experimentation. If one were to prove a law through experimentation, what is deemed a sufficient number of times? 

*Another question would be how can one prove something like the second law of thermodynamics?
 A: In reverse order, and to echo  CuriousOne's  comments, as you know already I'm sure, the second "law" isn't a law, more a general principle regarding the probabilities of the existence of certain quantum states.

My biggest question about this is about proof through experimentation. If one were to prove a law through experimentation, what is deemed a sufficient number of times?

There is nothing else but repeated experimentation, in other words, the standard reply might be that you are testing GR every time you turn on your GPS and you are testing thermodynamic principles each time you start your car engine.
As CuriousOne implies, we can only falisfy our current theories, and we can never cast them in stone. I have seen statements in Cosmology textbooks that say, in effect: "Some of what's in this book is wrong, and if we are really, really  lucky, most of it is wrong", as we have so much that still has to be explained by new ideas, such as why the entropy at the start of the universe was so low. Arrow of Time
A: This is a physics question and answer site.
Laws in physics are a distillation of experimental observations, and a foundation stone in the theories, mathematical models, built up in order to describe data and predict new behaviors. In a very real sense they are the physics axioms that connect mathematical formulae to physical measurements.
History of physics shows that physics laws change, are absorbed in larger and more descriptive mathematical theories.
The observational history of electricity and magnetism is a good example. Observations gave many laws, but the ingenious use of mathematics reduces  the initial assumptions/"axioms" to *"there exist electric and magnetic potentials which obey Maxwell's equations"*. What were "laws" before can be derived from the behavior of the equations. Only the Lorenz force remains as an independent "law/axiom" for classical electromagnetism.

My biggest question about this is about proof through experimentation. If one were to prove a law through experimentation, what is deemed a sufficient number of times? 

So one cannot "prove" laws, one can check the validity of the theory that has the law as an axiom. If a theoretical prediction is not validated, the whole theoretical construct has to be redefined, the mathematics changed ,and even the law changed. 
Take the mathematical model of flat geometry that fits well on city streets. "two parallel lines do not intersect" is an axiom for the mathematics, and the physical observations. Once one goes to large distances, the axiom is falsified because the measurements do not fit the model: spherical geometry is the mathematical model that fits the surface of the earth, and the axioms change.

Another question would be how can one prove something like the second law of thermodynamics?

When a more encompassing theory has been found that fits observations, it is often that what were "laws" from measurements can be derived from the mathematical formulation, for example  Amperes law emerges from the Maxwell's equations. In this sense it is "proven", but the wider framework should exist.
Thermodynamics is an emergent theory from an underlying particle level and in this sense, the inevitability of what are observational laws for thermodynamics can be seen to emerge from the statistical behavior of the underlying particle framework, as others have said.
