Terahertz (THz)-band communications are a key enabler for future-generation wireless communication systems that promise to integrate a wide range of data-demanding applications. Recent advancements in photonic, electronic, and plasmonic technologies are closing the gap in THz transceiver design. Consequently, prospect THz signal generation, modulation, and radiation methods are converging, and the corresponding channel model, noise, and hardware-impairment notions are emerging. Such progress paves the way for well-grounded research into THz-specific signal processing techniques for wireless communications. This tutorial overviews these techniques with an emphasis on ultra-massive multiple-input multiple-output (UM-MIMO) systems and reconfigurable intelligent surfaces, which are vital to overcoming the distance problem at very high frequencies. We focus on the classical problems of waveform design and modulation, beamforming and precoding, index modulation, channel estimation, channel coding, and data detection. We also motivate signal processing techniques for THz sensing and localization.