I just bought a new guitar. It has a plastic nut and it appears that the string slots are binding the strings (when tuning the string won't move suddenly it will make a "sprong" sound and move).

What can I do about this?
* Sand paper?
* A special file?
* Any tips?

Get a pencil and just kinda draw in the slots. You will end up with basically graphite in there that will help the strings move easier. Or you can go to a guitar shop and get some nut some of this> http://accessories.musiciansfriend.com/product/Big-Bends-Nut-Sauce-Tuning-Lubricant?sku=429800
If you start a reply with: I have never played one but I have heard good things about it! Your opinion is invalid.
Pencil lead. Take a pencil, (the kind you sharpen work best. As opposed to a mechanical pencil.), and scribble within each slot, until the slot is completely covered.
Pencil lead is made of graphite, which is very slippery. This should eliminate your problem. Try this before you do any sanding.
There's my way and the wrong way.