How to set about excavation?
Any excavation requires organisation, funding, effort, someone with archaeological experience in the team to ensure the clues are spotted, and a commitment to the post excavation (writing up). There are ways of achieving this. Local archaeological societies have very experienced members, getting university departments to assist, paying for a commercial archaeologist to oversee the project.
All archaeological excavation is destruction. Therefore one picks the location very carefully. Any excavation in to the earthworks will leave a scar so one should try to find a location where the earthwork has been destroyed on the surface (perhaps ploughed away) and drop a trench across the line, picking up the ditch. Excavating the ditch should provide sufficient dating evidence in the ditch to get an idea of when the construction took place and also the original character and scale of the ditch.
Excavating in the bank will also provide dating and might even reveal archaeology that predates the bank sealed beneath it. It might also reveal if the top was palisaded. But I would discourage that as least at this stage. I would encourage find a place where no visible damage is done so that the earthworks remains intact as far as possible.
Any section that is a scheduled monument is protected and cannot be excavated without the permission of the Historic England. They would almost certainly refuse permission until all the options that don’t involve digging into the scheduled monument had been achieved (i.e. a scheduled monument is the last place you dig).
If you are keen to dig, and can get the support (in all its guises) I would recommend that you look for a section that has been ploughed out and, with the land owner’s permission, find and excavate the ditch.
If in any doubt I would suggest your first step would be to get an archaeology ‘partner’ – possibly someone from a local archaeological society, who can help you gather and gauge the scale of the undertaking and the steps of the journey, the cost and the amount of muscle needed.