Check me out, being all crafty. I had a sweater that had a big hole in it but was otherwise fine, so I used that and followed this method.
http://abeautifulmess.typepad.com/my_weblog/2012/01/tips-for-sewing-sweater-knit.html
It looks a bit gnomish (particularly because it's red, but it's not bad for a first effort (and considering I hand sewed it). I may make mittens next.
Re: I made a hat last night
How resourceful of you! I am sure it came out nice even for a first attempt. Good luck on the mittens!