What's the difference between using the preterite and imperfect tenses?

Though the preterite tense is often described as the "past tense" of Spanish, the truth is that both the preterite and imperfect tenses translate to our use of the simple past tense in English. Whereas in English we don't make a distinction between the two, in Spanish you would use the preterite conjugation to describe a simple, one-time event in the past ("Ayer yo fui al parque," or "Yesterday I went to the park") and the imperfect conjugation to describe habitual actions or background information in the past ("Cuando yo era joven, siempre iba al parque" or "When I was young, I always went to the park").

How do I know whether to say "write" or "writes?"

In English, subjects and verbs have to match -- singular subjects get singular verbs, and plural subjects get plural verbs. You may know that nouns have an "s" at the end when referring to more than one, as with the word "girls" (though not always, as with "children"), but with verbs it tends be the opposite: singular verbs are what usually get the "s," as with the word "writes" (again, not with all verbs). Therefore, it's correct to say "the girls write" or "the girl writes," but it's wrong to say "the girls writes."

How does the past tense (e.g., John ate) differ from the present perfect tense (e.g., John has eaten)?

The past tense refers to a past event that may or may not necessarily relate to the present moment - for example, whether John ate yesterday, or John ate three weeks ago, has no bearing on whether he needs to eat now. However, using the present perfect tense suggests a relation to his present state - John has already eaten lunch, therefore he's not hungry right now.