Is it "described in" or "described on"?

Solution 1:

When used alongside the word 'described', the preposition 'in' would be the equivalent of either 'via' or 'inside'.

So, in the example you've given, the correct answer is 'in', because the methodology is described via (i.e. through the means of) the table/figure.

An example of its equivalence with 'inside' could come about if, say, a publication had run an article on the methodology, in which case you would likewise say that 'the methodology was recently described in The Notable Journal.'

To use the preposition 'on' with the word 'described' is to convey the medium by which the description was made, e.g. 'the methodology was recently described on paper in an issue of The Notable Journal.'

Notes: I'm English. As far as I know usage is the same in US English, but I'm not totally certain of it.

Solution 2:

"In" rather than "on" would be right. But I'm not sure "described" is the best word. A table obeys a certain logic, but doesn't actually describe the logic. I would say something like "the methodology is inherent in the table", or "embodied in the table", or "can be inferred from the table".