Suppose I learn enough Norwegian bokmål to be able to read books and newspapers well enough to follow what is happening, even if I would miss nuances and occasionally misunderstand something. I'm already there with Danish, so bokmål is not that far away.
Suppose I have not studied nynorsk explicitly.
How well would I be able to read nynorsk in this situation?
The short answer is that if you are fluent/advanced in Norwegian and can read Bokmål, then you will be able to read Nynorsk without much trouble.
In the situation that you are an intermediate reader of Bokmål, then it will be helpful if you know the major spelling differences between the two, as covered here and here. After knowing those "conversion" tricks, then there is the small matter of knowing some grammar differences, as mentioned here and quoted below:
Nynorsk grammar is probably a little more complex than Bokmål grammar, especially because (as noted by Magnus Itland) you must observe three different genders in nouns (masculine, feminine, neuter), whereas Bokmål allows the collapsing of the masculine and the feminine into a Common gender, morphologically like the traditional masculine. For instance, the suffixed "definite article" is -en for masculine nouns and -a for feminine nouns, so a traditionally feminine noun like bok (book) can in Bokmål become either boken or boka for "the book"; the former variant sounds more literary or upper-class, whereas boka connects more closely with the unpolished everyday vernacular of Oslo and the area around the capital. In Nynorsk, the form boka is obligatory, and carries no particular stylistic implications.
