Deleting an item from the Web Editor is usually as simple as clicking the Delete link next to the item's name and then clicking ok in the confirmation box that pops up.
However, if an item has other items under it (like an attached picture, or pdf) the Web Editor will not let you delete the item until you have deleted the items under it. Until this is done the delete link for items that have sub-items will be greyed out, with a number in parenthesis showing the number of sub-items the item has:
In this example the press release "Report Shows Imminent Extinction for Forest-Dependent Seabird" has one item under it, because a picture was attached to it. Until the picture is removed from this press release, the Delete link will remain greyed out.