(One thing to note first, these terms aren't universally accepted. Linguists like to come up with new terms, and some people might use "imperfective" or "continuous" where I use "progressive", or "preterite" or "aoristic" where I use "simple", and so on.)
Tense-wise, English has only two morphological tenses: past and non-past. These can be determined by looking at the first verb word in the phrase. "Will" + non-past, as a special augmentation, makes future. (But people often use the non-past for future events without "will": would you really say *"after you will arrive in Berlin"?)
If there's no other auxiliary (extra verb word), you have simple aspect. This is a sort of default form without anything special added.
If you replace the verb with "have" + past participle, you have perfective aspect. This indicates that the action was already completed, and you're talking about the effects that resulted. For example, compare "I ate" (simple action in the past) against "I have [already] eaten" (the action's finished, but we're talking about its effects in the present, so "have" is marked non-past).
If you replace the verb with "be" + present participle, you have progressive aspect. This indicates that it's an ongoing action, or an action that's extended over a duration. Again, compare "I ate" against "I was eating" (…over a span of time, during which something else happened).
Finally, if you replace the verb with "be" + past participle, you have passive voice. The direct object becomes the subject, and the subject is pushed off somewhere else.
Any number of these can be applied, in the order I listed them. For example, you can say "he will have been being fired": from beginning to end, this marks future tense, perfective aspect, progressive aspect, and passive voice.
The opposites of these don't really have well-agreed-upon names. So the easiest way to refer to 1 and 2 is "non-progressive", and the easiest way to refer to 1 and 3 is "non-perfective". None of these appear only in English, but in many languages the perfective and progressive are mutually exclusive, so the non-progressive non-perfective can be given a name ("aoristic"). But that's not the case in English, where you can mix and match them freely.