DH and I went on the Segway tour in July, so I can add a little.
First, there are 2 tour times now. When we did the tour, there was only one, but our tour guides told us they were to begin adding a second time slot a short time after our tour. I'm not sure about the times, but at least the first tour begins before the park opens.
Our meeting time was before the park opened, so we had to go to a designated entry and our names were on a list of people who could enter before the park opened. Tour participants meet in Guest Services in Epcot, then go to a practice room in the building where FountainView Bakery is. Practice in the room lasts for about 1 hour. The room is not open to the public and there are no windows, so other guests are not able to watch. During the practice time, you get familiar with how to get on the Segway, how to stop, start and ride it, going up and down ramps/inclines, etc. The class size is small and you get ample practice before venturing out. When we were there, they were still finalizing plans for how the two tours would work, but the plan was for the second tour to begin in the same practice room after the earlier tour had left for the WS portion of their tour.
After the hour of practice, the tour goes to WS, which is not open to the public yet at that time. There really isn't a way for family and friends to watch the tour. Seeing the tour is more a matter of luck and just being at the right place at the right time when the tour goes by. You don't know exactly when the group will leave the practice room to go to WS and they are really only "out" in areas open to the public for as long as it takes to go from the practice room to WS. The International Gateway is open for guests to walk from the Epcot resorts to Future World (along the UK/Canada side only) and on the other side of WS, the walkway is open from Mexico to Norway for guests who are going to the Princess breakfasts. Other than that, WS is closed.
While in WS, Segway Tour participants are with a guide and a Segway instructor and it's more like "Follow the Leader" than just rolling around WS by yourself. The tour guide leads, the rest of the tour follows and the instructor brings up the rear to keep the group together and help anyone with problems. It takes about 1 hour to go around WS; after that, the tour returns to the practice room.
It was a really neat experience and I would do it again or recommend it to anyone.