Conceptual framework is provided for some of the well known ideas relevant to the use of random numbers for sampling. Results on the efficient choice of d (the number of digits in the column of random numbers) are envisaged to be of use to the practitioner in designing a simulation exercise. The exact and appropriate methods of sampling in different situations are also given. Most of the work is limited to univariate populations, but briefly methods are indicated for dealing with bivariate or multivariate cases.