Fast Fourier Transform (FFT) is essential in digital signal processing (DSP). The AI Engine array of very-long instruction word (VLIW) processors with single instruction multiple data (SIMD) vector units are highly optimized for compute-intensive DSP algorithms such as FFT and Discrete Fourier Transform (DFT). This tutorial illustrates several different techniques for mapping FFT and DFT algorithms to the AI Engine array, including the Stockham FFT used in AMD Vitis™ DSPlib, hand-coded variants implemented using the AI Engine API, and a direct form DFT using vector-matrix multiplication that can be efficient on AI Engine for small point sizes.