* ten/ta/to = der/die/das (the)
* nějaký/nějaká/nějaké = (irgend-)ein/eine/ein (a, some)
In my course there's the example “nějaká paní se ptá na cestu" (A woman asks for the way). Not sure what is different if the nějaká is left out.
* ten/ta/to = that, not “the”; I.e. literally or figuratively pointing (including e.g. referencing previously mentioned object and not wanting to repeat it)
* nějaký etc. - some, not “a”, i.e. explicitly strongly expressing vagueness. “A” in English is automatic grammar construct, “some” is explicitly expressing uncertainess. That sentence would correctly be translated as “SOME woman asks for directions” - I.e. a woman you don’t know, some rando that walked in the shop for example. A more real sentence: “some woman is asking for you” (you don’t know her, never seen her, she just walked in and asked for your colleguae), “nějaká paní se po tobě ptá”. You would use “a” in English here, it warrants clarifying the situation with “some” - and in Czech, that’s the only situation when you need these, when you are pointing to/referencing something or expressing vagueness.
> ten/ta/to
are you sure it's not "that" (dies(e,es,er)) instead of "the"?
> Not sure what is different if the nějaká is left out.
I'd interpret it as "The woman asks for the way.", i.e., a particular person is contextually implied. Otherwise it doesn't make sense.
EDIT: alternately, it describes an abstract event of woman asking for directions. Putting it as "paní se ptá na cestu" would make perfect sense in, say, a movie script.
Say a friend observed you from the other side of the street talking with her, approached you and asked what was that about.
You could say "[nějaká] paní se ptá na cestu" both with and without "nějaká". WITH "nějaká" you'd be emphasizing it was a random woman. WITHOUT "nějaká" it'd be that particular woman he saw you talking with. though, I'd use "she" for describing the event, i.e., "she asked for the way".
About dieser/diese/dieses, that would be tento/tato/toto (this/that here).
It's all a kind of ouroboros of languages - if something gets simplified, something else appears there