It is really hard to tell whether to use the definite or indefinite conjugation. Can anybody give a few useful hints?
You use the definite conjugation when the sentence has a definite direct object. An direct object is considered definite if:
It is preceeded by a definite article: Kérem a kenyeret- I would like the bread. / Contrast this with the indefinite conjugation: Kérek kenyeret- I would like bread.
It is modified by or consists solely of the demonstrative pronouns. Ezt kérem- I would like this (one). Látod azt az autót?- Do you see that car?
It is a proper noun: Szeretem Zsuzsát- I love Zsuzsa. Jól ismerjük Budapestet- We know Budapest well.
It has a possessive ending: Kérem a telefonszámodat.- I would like your telephone number.
It is a third person pronoun Látom (őt/önöket)- I see him/you. (Note: The pronoun does not have to be stated. The definite conjugation will suply the meaning of the third-person direct object.
It is the reciprocal pronoun: egymás "each other." Látják egymást- They see each other.
It is the modifier "melyik" or it is preceed by "melyik:" Melyiket kéred?- Which one would you like? Melyik könyvet kéred?- Which book would you like?
Laslly, the definite conjugation is commonly found with verbs in the main clause of a sentence when that verb introduces a subordinate "hogy" clause. (Azt) Látod, (hogy) ott van a gép- Do you see (that) the plane is there? (Azt) Tudja, (hogy) mikor érkezik a gép?- Does she know when the plane will arvive?
Which one of those relates to this sentence? What is the implied direct object of 'nem teniszezem'?
None of them.
teniszezik is an ik verb; those are (usually? always?) intransitive but have the -om -em -öm ending in the first person singular form (and the ik ending in the third person singular form).
So this is an indefinite conjugation that just happens to look like a definite one.
Thank you; yes, I realised this shortly after posting the question. These forms have not been mentioned in the notes yet; if any members of the Hungarian team are reading this—it would avoid a lot of confusion if you were to warn us about these verbs earlier on!
At least eszik and iszik are transitive, and a few more of those verbs can take a direct object. But generally they're intransitive, yes.