To harness the full benefit of new computing platforms, it is necessary to develop software with parallel computing capabilities. This is no less true for statisticians than for astrophysicists. The R programming language, which is perhaps the most popular software environment for statisticians today, has many packages available for parallel computing. Their diversity in approach can be difficult to navigate. Some have attempted to alleviate this problem by designing common interfaces. However, these approaches offer limited flexibility to the user; additionally, they often serve as poor abstractions to the reality of modern hardware, leading to poor performance. We give a short introduction to two basic parallel computing approaches that closely align with hardware reality, allow the user to understand its performance, and provide sufficient capability to fully utilize multicore and multinode environments. We illustrate both approaches by working through a simple example fitting a random forest model. Beginning with a serial algorithm, we derive two parallel versions. Our objective is to illustrate the use of multiple cores on a single processor and the use of multiple processors in a cluster computer. We discuss the differences between the two versions and how the underlying hardware is used in each case. Parallel Statistical Computing with R: An Illustration on Two Architectures