Splitting the plants can be done any time of the year. The spring is probably better as you can see the buds in the crown. You want to split the crown so there are a few buds in each "new" plant. You can dig up the whole root or split it in place. If you did up the whole thing be sure to put some back in the same place. It must have been a good place for the plant because it got big enough to split.
If you do get rhubarb from neighbors, buy it from a greenhouse, or start from seed, when you transplant it in your garden but sure not to cover the crowns completely. I guess the best way to explain it is to make the new planting look pretty much like the old one. It's one of those things that you don't want too much sticking out of the ground but you don't want to bury the crown either. Rhubarb does best in full sun with plenty of water. If you must put it in a spot without full sun you should put it somewhere in the garden that will get sun for at least a few hours. It will grow in full shade as well but will look pretty scrawny.
Thanks to generous donations from our neighbors Paula Zawadi, Phyllis Rude, and the Hobbs family, we now have rhubarb plants underneath the whole west fence line of the garden and under the rose bushes in front of the church. The garden is well fixed for rhubarb now. This should be the first harvest of 2019.