As already mentioned, the expo itself is free, and open to anyone who wants to attend. The easiest way to get there usually is to take the runDisney provided buses that depart from the host resorts pretty much every 10-20 mins. If I recall correctly, every on property resort is a host resort for Princess Half weekend. If you are in a park, you would either need to drive over, or go to a resort and then take an expo bus. WWoS doesn't normally have scheduled transportation, I think that DHS is the only exception to this and that may be suspended when the expo buses are running.
Speaking from experience from Marathon weekend past weekend (and other expos in past years) the New Balance process can be smooth, or chaos. The most recent one, I registered myself Weds AM at 6, and got a Group 1 return time. Basically when the expo opened. I registered my wife about 3 mins later, and ended up in like Group 12, with a 2:30 or something return time. Got to the expo about 9:45, and hadn't received a text message. Went to the check in location, and it said they were on Group 2 already. There were about 30 people in line, most from Group 1 who said they never got their text either, and we had about a 10 minute wait. Was back in the same area on Thursday at about 10, and there was absolutely no line.
If you aren't running, you won't be able to sign up until the second day, as already pointed out. If you hop on right at whatever time they open registration, you should have no problems getting a time. The nbvirtualqueue.com site only shows the sellouts from the Star Wars weekend, but I think Marathon weekend was similar. Basically the common middle of the road sizes sold out towards the end of the weekend.