You wont be able to put the videos onto youtube directly from osu!
First all of when you finish a map make sure you have the "save local replay" box checked
http://puu.sh/7USLThen you will need some sort of video recording software (such as fraps, or whatever you want to use) and record the replay of you playing the map, then you will be able to add it to youtube. There have been discussions about allowing videos to be uploaded straight from osu!, but it is unlikely to happen any time soon (if ever).
This thread should cover most of it
viewtopic.php?f=13&t=18112