So, my sister's wig arrived but has no style what so ever to it.

Does anyone have any tips on how I can style it to look remotely like Kraehe's wig in Princess tutu. I've had one persone mention to be about heating it up and doing it that way. But are there any other tips.

Oh cripes..in at the deep end.
Yes you have to use heat but not severe heat eg no hot irons.

The only wig I re-styled so far was my Nehelenia wig. I bought extra long extensions and had to turn them from straight extensions into wavy/curly ones - The way I did it is to wrap the extensions around a wooden pole (like a roller) and then used my wallpaper steam-stripper on them like a clothes steamer..just use the hose without the large plastic wallstripper attachment. If you try this be carefull though and use thick gloves to hold the tube because steam and boiling water spit out of the hose.. Anywho yeah, so steam will set the fibres. Then I dried them with the hair dryer on moderate. When I took the extensions off the wooden pole they were reeeeally curled. ^_^
So that's how I did mine.

Have a read of this help thread, there's a lot of relevent stuff.
http://www.cosplay.com/showthread.php?t=132516