This one is probably fairly obvious for native speakers, but I'm always confused. I am writing an article and I want to say that such and such methodology is described in/on a table, a figure or a scheme.
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.
Since the table here is a row by column arrangement which contains information, described in will be used. This is because the information is in the table. If the table was a flat surface with legs (physical table), the correct form would be described on.
In general, the preposition on and at is used when we address a table.
Eg. Food is on the table. We are sitting at the table.