Is there a concise way of learning the core Monte Carlo Methods from resources available online?
This leads to my next question which is what are the core ideas to learn in Monte Carlo methods?
There is Monte Carlo Simulation and there is Monte Carlo Simulation. If you are referring to a simple question like simulating dice or calculation of $\pi$ or even vanilla option price calculation, it is one thing and "concisely" available. I recommend get a gist of small examples from CS books and then get on with finance.
But if you are referring something more advanced applications using particle filtering, variance reduction, gibbs sampling, Metropolis-Hastings, MCMC, sequential MC, quasi-MC etc. I recommend you to look for CS books first and then use them on finance.
Well luckily I got both courses at university here are some sources.
My Monte Carlo course's (I am not the instructor, just took the course) home page, you can still download from the links.
Hull's book Options, Futures and Other Derivatives is also a good reference.
Tools for Computational Finance is a bit advanced and finance-y.
There are also online courses for it. MIT OCW has one.
The core idea of MC is trial and error. As you venture on the MC way you see smarter ways of doing it.
My advice of the path to learn is
Caution: Monte Carlo is both computationally and mathematically challenging. The 'basics' are really fun and basic but to significantly benefit from them you need to invest heavily on your learning.
Your question is too general because Monte Carlo methods differ quite a bit. It's driven more by the problem you are trying to solve, significant result sets, etc, etc.
You would either have to
My first experience with them was trying to solve a progressive jackpot game for a friend.
Sometimes, you just have to throw yourself into code in order to learn.