To delete a project just click on the “actions” icon on its right, then “trash”. You will have to confirm this action.
You can find the "actions" icon next to the project name in the project tree on the left, or in the working area.
In case you want to undo this and move the project out of the trash, just go to "Trash" (4th icon at the top of the project organizer, so left of the page, close to the main menu of the application).
There you just need to select “restore” by clicking on the “actions” icon on the right of the project name.
Note that when clients just have one projects and you move them to Trash, the whole client goes there (so no empty clients are allowed in the project tree). We did it like this to avoid having empty items around, but let us know if that bothers you!