This tutorial aims to provide an intuitive introduction to Gaussian process regression (GPR). GPR models have been widely used in machine learning applications due to their representation flexibility and inherent capability to quantify uncertainty over predictions. The tutorial starts with explaining the basic concepts that a Gaussian process is built on, including multivariate normal distribution, kernels, non-parametric models, and joint and conditional probability. It then provides a concise description of GPR and an implementation of a standard GPR algorithm. In addition, the tutorial reviews packages for implementing state-of-the-art Gaussian process algorithms. This tutorial is accessible to a broad audience, including those new to machine learning, ensuring a clear understanding of GPR fundamentals.