Fields can be deleted in two ways:

In the Desktop FieldAgent™ Application

In the overview map view, find the field in the "All Fields" expander box on the lower right corner of the screen. Then, from the field's gear menu, choose "delete".

Via the Web admin console

Login with your user credentials to Navigate to "Fields" (in FieldAgent™) in the left-hand menu. Find the field you wish to delete, and from the field's gear menu, choose "delete". 

Changes made through the web will be reflected on any desktops connected to your account following the next sync event.