Hi there! I just jumped into your account and took a look. In order to delete campaigns, you have to select the campaigns that you would like to delete via the check box to the left of the campaign. Once you do this, a drop down arrow will highlight at the top right hand corner of the table which will allow you to delete the selected campaigns.
If you were in the new grids view, you would have a slightly different experience. You would still select the campaigns that you want to delete but an archive button would appear about the mailings.