The first map the OP linked to plus a little bit of colloborating at google maps is the best source of info.
As the other poster said, there is pretty good signage, and for the majority of it, you are on a seperate bike path. There are however, a couple unusual apsects:
- The NE missing link. From about Huron and the river road, to Stinson and St. Anthony Parkway, the train is not yet completed. I believe construction has begun but I don't know when it is expected to finish. You can actually see the missing link on the map pictured in the other answer, in the Northeast section.
- A section of W River road near Franklin I believe is still closed due to the landslide a year or two ago (2014 or 15).
- There is a not very thouroughly enforced but still present 10mph speed limit on all the bike paths, which is ridiculously slow for most riders. However, with the exception of the roads around the lakes, the other roads comprising the GRSB have all been paved recently so are pretty good riding, and they have 25 mph (which no motorist obeys) speed limits on them. The roads around the lakes aren't as smooth but they are still good enough.
- The previous point is important during nice weather because it will be very busy, and much of the traffic will be families with kids rolling along at 3mph, roller bladers, and other people that aren't supposed to be on the bike path but they'll be there anyway. So expect to take the roads in nice weather anyway.
Once a year the Minneapolis Park Board puts on the Grand Rounds Scenic Bike Tour, which is an opportunity to ride the whole path in a big group.
Source: Minneapolis resident.