Good data to start could be the human connectome project:

http://www.humanconnectome.org/data/

But even before that, you should probably start with some google searching to learn about how people model functional networks, period.  For example, I did a quick search and get results like this:

http://arxiv.org/pdf/1105.4705.pdf
http://journal.frontiersin.org/Journal/1...

Then you should make it your goal to download a data set, and do a few simple kinds of analysis.  Processing this kind of data is a career in itself - you can follow tutorials for software like SPM (in Matlab), FSL (linux), or freesurfer.  There is also the "conn" toolbox from MIT in matlab.  You will probably want to try a simple seed based approach (eg, define regions of interest in the brain, calculate correlations), and  unsupervised approaches that decompose the data (eg, ICA).  There are toolboxes everywhere for these kind of things, and it's probably best to get familiar with most of them, and ask people about what they like, so you can form your own preference.