I would say it's "take the subway", although I'm not sure why. In general when talking about means of transport we use the definite article "take the train", "take the bus", "take the subway", but there are exceptions, as we say "take a cab/taxi", using the indefinite article.

Usually "take the subway" because typically there's only one subway system in a particular city. There are circumstances when you might use "take a subway", but if you're giving directions, then "take the subway" is most likely correct.

This isn't my 'native language', but I don't see any reason to use a singular indefinite article ('a') here. 'Subway' isn't a single object (like a train or a bus). The word 'subway' refers to the whole system within a particular city. So you'd say either 'take the subway' (meaning use the system) or 'take a subway train' (meaning one train).

take the subway