This review considers methods of nonlinear dynamics to apply for analysis of time series corresponding to information streams on the Internet. In the main, these methods are based on correlation, fractal, multifractal, wavelet, and Fourier analysis. The article is dedicated to a detailed description of these approaches and interconnections among them. The methods and corresponding algorithms presented can be used for detecting key points in the dynamic of information processes; identifying periodicity, anomaly, self-similarity, and correlations; forecasting various information processes. The methods discussed can form the basis for detecting information attacks, campaigns, operations, and wars.