Hi there,
I started this process for you, and all you need to do is finish up with your registrar :)
You're going to get an email shortly with an Authorization Code. You can see what it will look like here:
http://en.support.wordpress.com/domains/transfer-domain-registration/#send-the-transfer-authorization-code
This page also contains the next steps you will have to complete with your new registrar.
You'll get emails at each new step, so make sure to read them carefully, because each will include some sort of activation or verification link. If you get one that's just a head's up with no link, that's fine, too :) Just make sure that in each one that does require your approval, you are able to give it, otherwise the transfer won't go through. The process usually takes a few days, with emails slinging about, so it's not like you have to sit next to your computer waiting for emails (they won't expire), but I would try to take care of them about once a day.
Here is the specific information from GoDaddy:
http://support.godaddy.com/help/article/1592/transferring-domain-names-to-us
Just let me know if you hit a snag!
Cheers! (PS, I have 13-mo-old twins myself, so I totally understand how stuff gets prioritized differently now :))