Which one is correct?
A partir de ahora, voy a hablar en español.
Desde ahora, voy a hablar en español.
In meaning I think both are close to "from." Are there any specific instances where one cannot replace the other.
A partir de is used when an action is going to take place starting from that point on. You can indicate the end by using hasta.
Desde means the same thing as a partir but the difference is that desde is used for actions that have already taken place and are still valid in the present or a specified point in time (you use hasta to indicate the end).
So which one is correct? It's difficult because of the ahora but for me as a native speaker it sounds more natural "Desde ahora...".
To simplify that.
Desde is more like "since" (in the temporal sense only).
You would not say, for instance:
You would/could say:
Desde works nearly everywhere, but a partir de only really works with sustantives.
"A partir de" is used frequently for resolutions, either personal resolutions like your example or "lawful" stuff ("a partir del lunes, las horas extras estarán prohibidas" [from Monday on, working overtime will be illegal]). It's also more natural if the point of time is just now or in the future, desde seems more natural for the past (i.e. hablo español desde el mes pasado; hablaré español a partir del mes que viene).
Please keep in mind that not every nd word in Spanish has a 'finite' translation form and that it can have different meanings in regards to colloquial differences. In Mex/Spanish, the direct translation of the phrase = 'apart from' = <----these 2 words together are the equivalent of the single English word 'apart' and are usually used in reference to distinguishing a single characteristic which sets it apart from the rest. The word <----means from and in this case, the two words together would mean 'apart from'. Although the word usually means 'from', in this case, it can also be used as a point of reference and that can be in the form of juxtaposition as well as Geo-location and in abstract form as opposed as to the finite. The Mexican word can mean either from or of, depending on the content or object of the sentence and can be used both in the abstract form as well as the finite. The direct translation of the Mexican word is both 'of' as well as 'from' and can also vary depending on the content and object of the sentence.