What is the easiest and fastest way I can take (and pass) a calculus course?

The easiest way is to learn calculus! You should start with the calculus of finite differences, an intro to calculus from this point of view appears in my answer here: How can/does calculus describe the movement of a particle?

The basic idea is that you want to define the notion of "difference" and "sum" of a sequence. The difference of a sequence like


is the difference of successive terms:


in equations, $(n+1)^2 - n^2 = 2n+1$. The fundamental theorem here is that if you add up the differences, you undo the operation of taking the difference:

$1 + 3 = 4$

$1 + 3 + 5 = 9$

$1 + 3 + 5 + 7 = 16$

etc. This is the fundamental theorem of derived sequences.

Calculus does the same thing, except with infinitesimal displacements. So when you are thinking about a function like $x^2$, you consider $(x+dx)^2$, where "$dx$" is very little. The coefficient of $dx$ when you expand it out is the derivative.

The analog fundamental theorem is the theorem that the integral of the derivative is found from the original function. It's very obvious and easy to learn, but if you skip the finite differences, it can be daunting.