Depending on the amount, a license would be required.
Here's a link to current limitations: https://www.nrc.gov/reading-rm/doc-collections/cfr/part030/p...
Link regarding exempt amounts:https://www.nrc.gov/reading-rm/doc-collections/cfr/part030/p...
Ah interesting. Apparently there is no exempt quantity of Cf-252.
Well I just found out that I was grossly underestimating the danger of handling Cf-252, given its half-life.
Look what ORNL used to transport 1g: https://en.m.wikipedia.org/wiki/Californium#/media/File%3ACf...
Yeah. A single fission event can generate 2-4 neutrons, so even a tiny spec can be pretty dangerous.
Here are the drums used for shipping much smaller amounts:
http://www.frontier-cf252.com/custom-type-a-packaging-radioa...
As far as who can buy it and what the approval process is? I imagine there are controls in place. I never inquired about that.