A domain transfer will generally take a few days, but the timing depends on your current registrar (GoDaddy - the company with which you manage your domain today) and the status of your domain. I know in the past when I've transferred domains over they usually take at least five days. You will be able to check the status of the domain transfer here http://inv.lv/R7KH08 in the DH panel.
As always if you need any further detailed help with your account, you can click here http://inv.lv/xplNd3 and our support team will look into it for you right away
Hope that helps,