Wavelet transformation works by decomposing a signal into a set of basis functions called wavelets. These wavelets are localized in both time and frequency, allowing for a more detailed analysis of the signal. The two main types of wavelet transformations are the Continuous Wavelet Transformation (CWT) and the Discrete Wavelet Transformation (DWT). CWT is used for a detailed analysis of the signal, while DWT simplifies the data for computational efficiency.