So far there was no way to upload music from a google computer (chromebook) to google music. Which was somehow odd.
Text below is obsolete now. Google music is now supporting uploads from chromebook (even from the gdrive). Thanks to the developers. More details at google plus post here.
Login to google music. Go to the settings menu (icon on the right) Select the lab item Enable the lab function as shown below
5. Wait some seconds (and enjoy the picture shown below)
6. Select your music import folders or just drag them into the window shown below
Another nice feature developed by google to keep the chromebook in the game (at least at their own music portal).