How to model random variables?

I want to know how to model random variables using "basic operations". The only random function I know, at least for C, is rand(), along with srand for seeding. There probably exists packages somewhere online but lets say I want to implement it on my own. I don't know if there are other very common random functions, but if not, lets just stick with rand() and the C language.

rand() allows me to pseudo-randomly generate an int from 0 to RAND_MAX. I can then use mod to get an int in some range. I can next mod 2 to choose a sign and get negative numbers. I can also do rand()/RAND_MAX to model values in the interval (0,1) and shift this to model Uniform(a,b).

But what I am not sure about is if I can extend this to model any probability distribution and at what point do I have to worry about accuracy especially when dealing with infinities and irrational probabilities. Also, this method is very crude so I would like to know of more standard ways using basic tools if any.

A simple example:

I have the random variable X such that Pr(X = 1)=1/pi and Pr(X=0)=1-1/pi. Since pi is irrational, I would approximate the probability of getting 1/pi with rand() and choose X=1 if I get an int from 0 to Round(RAND_MAX*1/pi). So this is approximating twice, once for pi and another time for rounding.

Is there a better approach? How would one go about modeling something more complicated such as a continuous random variable on the interval (0,infinity) or a discrete random variable with irrational probabilities on a countably infinite set. Would my approach still work or would I have to worry about rounding errors?

EDIT: Also how does the pseudo-randomness instead of randomness of rand() change things and how would I account for these changes?