De-embedding would be an alternative, but only if you already have the adapter's S-parameters.
What parameters should I measure?
Simply measure the S-parameters of the adapter (S11, S21, S12, S22).
[ The catch, however, is that you need calibrated reference planes where the adapter can be mechanically inserted.
E.g. For an N to SMA adapter, the VNA needs one calibrated SMA port and one calibrated N port ]
Is there a good tutorial...
The 'VNA Bible' is the Handbook of Microwave Component Measurements: with Advanced VNA Techniques by Joel Dunsmore.
You'll find a lot of useful information on the web, too.
I have a shitty SMA cal kit that came with a nanoVNA, but if it's profiled well with the good N cal kit I have, then it should be usable, right?
How can you characterize the SMA kit if the calibrated VNA ports are N-ports where you cannot attach them?
You need a "golden standard", either a characterized SMA kit, or a characterized adapter.
Well, up to, say, 300 MHz, you can probably live with 'ideal' standards—meaning you treat them as ideal and just measure the R
DC of the Load. But at 3 GHz, the parasitic effects and the electrical length of the standards are no longer negligible, making proper kit definitions essential.