Here we try to compile a list of background reading/studying material. If you know of good papers or other material, please add it by clicking on the edit button.
A comprehensive introduction in the neurophysiology and biophysics of EEG (also relevant for MEG) is given in Electric Fields of the Brain: The Neurophysics of EEG, 2nd Edition by Paul L. Nunez and Ramesh Srinivasan.
Steven J Luck, An Introduction to the Event-Related Potential Technique, MIT Press: 2005, ISBN 0262621967. This book is reviewed here: Peter Hagoort (2006)Event-related potentials from the user's perspective; Nature Neuroscience 9, 463.
The brain in time: insights from neuromagnetic recordings by Riitta Hari, Lauri Parkkonen and Cathy Nangini gives a comprehensive introduction to MEG.
MEG: An Introduction to Methods. by Peter Hansen, Morten Kringelbach, Riitta Salmelin.
Gross J, Baillet S, Barnes GR, Henson RN, Hillebrand A, Jensen O, Jerbi K, Litvak V, Maess B, Oostenveld R, Parkkonen L, Taylor JR, van Wassenhove V, Wibral M, Schoffelen JM. Good practice for conducting and reporting MEG research. Neuroimage. 2012 Oct 6. pii: S1053-8119(12)00989-5. doi: 10.1016/j.neuroimage.2012.10.001. [Epub ahead of print]
Terry Picton et al. published the Guidelines for using human event-related potentials to study cognition: recording standards and publication criteria in 2000.
The OHBM Committee on Best Practice in Data Analysis and Sharing (COBIDAS) wrote a report on Best Practices in Data Analysis and Sharing in Neuroimaging using MRI. Although this is on (f)MRI, the parts on subjects, tasks and data analysis are also relevant for EEG and MEG.
Nature has a Reporting Checklist For Life Sciences Articles that is helpful to consider when you write your manuscript, also when you don't plan to submit it to Nature.
Analyzing Neural Time Series Data: Theory and Practice. by Mike X. Cohen.
Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques Donald B. Percival and Andrew T. Walden, 1993.
Bruns A. Fourier-, Hilbert- and wavelet-based signal analysis: are they really different approaches? J Neurosci Methods. 2004 Aug 30;137(2):321-32.
Michel, C.M. et al. EEG source imaging. Clin Neurophysiol, 2004; 115(10):2195-222.
Baillet, S and Mosher, J.C. Electomagnetic Brain Mapping IEEE Signal Processing Magazine, 2001; November:14-30.
The following paper is a review and gentle introduction into beamforming: Hillebrand A, Singh KD, Holliday IE, Furlong PL, Barnes GR. A new approach to neuroimaging with magnetoencephalography. Hum Brain Mapp. 2005 Jun;25(2):199-211.
Schoffelen JM, Gross J. Source connectivity analysis with MEG and EEG. Hum Brain Mapp. 2009 Jun;30(6):1857-65.
For an introduction to MATLAB have a look at the excellent tutorial and exercises in MATLAB for Psychologists.