Hi Rubberduckey,
What you need to do is be very careful not to touch either of them. The brown wire is live and the blue is neutral (there are usually 2 blue wires that come from you ceiling into your light fitting). Does the light still work in its current condition? If so, you just need to screw the casing back to the ceiling. If you are unsure you should really get an electrician because electricity is very unforgiving with "have a go Joes"
Does your house have trip switches? If not, you need an electrician for safety. If you have trip switches, you can turn off the power to the whole house by flicking the master switch (this is usually a big black switch that you pull down). Make sure you do this in the morning so light doesn't become an issue, DO NOT DO THIS IN FADING LIGHT!
After flicking the master switch, flick on and off several light switches to make sure there is no power going to the lights (if you just try one light there is a chance that the bulb has blown and there is still power going to the lights, then you touch the wire and BANG!, weekend ruined!!)
When you are sure the power is gone you can screw the casing back to where it was. When you are happy that it is back to normal you can restore the power by flicking up the master switch in your switch box. If there is a short in the wiring or anything is a miss the trip switch marked "lights" should trip itself off.
Again, if possible please get someone with electrical knowledge to perform this (i know its impossible to get an electrician for small jobs but we all know someone thats handy with these things)
Good luck!