You use ने only in certain tenses (simple past, past perfect, present perfect, future perfect). In these tenses, transitive verbs (verbs that can take one or more object) agree in gender and number with their object(s) and not the subject. You need to add ने to mark the subject of the transitive verb.
Indefinite past (simple past) - 'The cow ate leaves' - गाय ने पत्ते खाये। (Note that the verb खाये is in the masculine plural form. This is because it agrees with its object which is पत्ते and not the subject गाय which is feminine)
In the other tenses, verbs (both transitive and intransitive) agree with the gender and number of their subject. So, ने is not required.
Present continuous - 'The cow is eating leaves' - गाय पत्ते खा रही है। (Note that the verb is in the feminine form because it is agreeing with the subject rather than the object)
The course doesn't cover the past perfect and future perfect currently.
Since English also has all these tenses, I'll provide examples instead of definitions.
Past indefinite (Simple past):
'I went', 'I ate'
मैं गया, मैंने खाया
'I had gone', 'I had eaten'
मैं गया था, मैंने खाया था
'I have gone', 'I have eaten'
मैं गया हूँ, मैंने खाया है
'I will have gone', 'I will have eaten' मैं गया हूँगा, मैंने खाया होगा
(Note: I have listed only the basic tense forms. Some of these tenses make sense only when the reference times are provided in the sentence inself or well defined through context).