Perfect Tenses

It's difficult to properly put this grammar point into words, so I'm going to start off with a couple examples to make it more clear. These are pulled right from Genki.

私は昨日宿題をしました。
I did the homework yesterday.

私はもう宿題をしました。
I have already done the homework.

In these two sentences, the English translations contain past tense and past perfect tense (i.e., did vs. have done). However, it's critical to note that in Japanese, the same verb tense is used in both cases - past tense. This is because affirmative past tense can be used for both plain past ("I did this") and past perfect ("I have done this"). Words like 昨日 and もう are used to distinguish the two.

The same is not true for negative past tense. In negative sentences, simple past is used for past tense, while ている form is used for past perfect. Again, these two examples are pulled from Genki.

私は昨日宿題をしませんでした。
I did not do the homework yesterday.

私はまだ宿題をしていません。
I have not done the homework yet.

Here's the way I see it: while plain past is describing something that simply did not get done, past perfect is describing something that's "in progress" of not being done (but you still intend to do it). After all, that's kind of what's implied in English when saying something like "I have not done the work yet" (but will get to it eventually).

This tense can be used with transitive and intransitive verbs, or as Genki calls it, changes and activities. It's also important to note that まだ is used here for the "not yet" part.

芝居はまだ始まっていません。
The play has not yet begun.

アリスは今朝まだ起きていない。
Alice hasn't woken up yet this morning.

スバルはまだ指輪を買っていない。
Subaru hasn't bought me a ring yet.

リーさんはまだ勉強していません。
Lee-san hasn't studied yet.