"That child came to Delhi."
Translation:वह बच्चा दिल्ली आया ।
ने is only used with transitive verbs (verbs which can take a direct object).
आना is intransitive and conjugates with the subject in all tenses.
Note: In this sentence, दिल्ली seems like it is a direct object of आया but it is not so. There is an implicit postposition ('ghostposition') between them. This can be seen more clearly in the English sentence where there is a 'to' between 'came' and 'Delhi'.
You use था in many tenses:
1. Past habitual: Used to talk about habits and repeated events in the past.
Eg: वह बच्चा दिल्ली आता था - That child used to come to Delhi
2. Past continuous: Used to talk about an ongoing action at a moment in the past.
Eg: वह बच्चा दिल्ली आ रहा था - That child was coming to Delhi
3. Past perfect: Used to talk about an action completed before a reference time in the past.
Eg: वह बचा दिल्ली आया था - That child had come to Delhi