Acquiring the necessary background for research
In my experience, it is better to learn stuff as you need it. Otherwise, you don't have the motivation to really "get" it, and there is always the risk of getting lost in the forest of interesting stuff out there (that in the end is of no use). Be at the lookout for results that could help you (Google or citeseerx or ..., or even this site, are your friends).

Another piece of advise: Start writing right now. Editing your ramblings into something coherent later on is easy, sitting in front of a blank screen with writer's block when the deadline approaches is extremely painful. Write down what you do right now; if it works out it stays for later, if not it gets erased (and you don't get embarassed by your dumb attempts ;-). That way it doesn't happen to you that you know something is right, but don't remember why... and have to redo lots of work (happened to me!).

Make a short (3-4 line) summary of each paper or other reference that looks relevant, add it to your bibliography. Reading the stuff so you are able to extract what is relevant to you helps understanding the stuff, the summaries help in locating material later. And the collection of summaries will be your chapter on state of the art (after cleanup).

As a final comment, use LaTeX (it looks much nicer, has very good handling of bibliographies ;-), and perhaps asymptote for figures (it is a bit hard to learn, but has C++-like syntax to manipulate points and define lines, and produces excelent results). Put the whole stuff under version control (my favorite is git, but use whatever you are confortable with). That  way you'll be able to have an up-to-date backup (preferrably on some other machine!), and go back if you really mess up (Murphy's lat assures us you will).