To literally see the Delta you can go on a 'sightseeing' flight for a few hours in a very small prop plane; the same ones that are used to transport people to and from lodges.

You can also take a mokoro trip onto the waterways near Maun or a powered boat trip towards Chiefs Island in the delta. Or do a guided day trip into the public Moremi Game Reserve; or a longer mobile safari. These options will be subject to availability and most likely you'll be required to find a minimum number of people. Many accommodations organise these trips, but particularly the backpacker/independant traveller places like Old Bridge, Audi Camp, Okavango River Lodge.

You can also do mokoro trips along the western side of the panhandle, but obviously you need to get yourself there.