How to calculate realization of a random process?

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I am newly learner of subject of stochastic processes and my mind is full of questions. Hopefully I can ask one of them in a correct way.

Suppose that X is an random variable which follows exponential distribution with parameter $\lambda$. (Let's say X is number of the cars in the park) For a while of period lets say 30 days, I check the number of the cars and note the random values for day 1, D1=X1, D2=X2,...,D30=X30.

How can I compute the realization (x) of this random event?

With which concept ?

Can I do it Poisson process etc?

As I said, I am newly learner and all the informations are welcome.

Thank you.