The EEG (Electroencephalogram) signal indicates the electrical activity of the brain. They are highly random in nature and may contain useful information about the brain state. However, it is very difficult to get useful information from these signals directly in the time domain just by observing them. They are basically non-linear and nonstationary in nature. Hence, important features can be extracted for the diagnosis of different diseases using advanced signal processing techniques. In this paper the effect of different events on the EEG signal, and different signal processing methods used to extract the hidden information from the signal are discussed in detail. Linear, Frequency domain, time - frequency and non-linear techniques like correlation dimension (CD), largest Lyapunov exponent (LLE), Hurst exponent (H), different entropies, fractal dimension(FD), Higher Order Spectra (HOS), phase space plots and recurrence plots are discussed in detail using a typical normal EEG signal.