In English there are "strong" and "weak" verb forms: for example, "go, went, gone" (strong) and "learn, learned, learned" (weak). Similarly, in Greek some verbs appear in the past tense as "strong" verbs (second aorist), while others appear as "weak" (first aorist). This will become more apparent once both forms of the aorist have been introduced. Inititally it should be pointed out that both first and second aorist verbs function in exactly the same way, although they are formed differently.

The aorist is a secondary tense like the imperfect, and is therefore built upon secondary suffixes.

Also like the imperfect, the aorist has the past time morpheme or epsilon augment and therefore expresses action that as past tense.

The aorist is distinguished from the imperfect in that it expresses simple past action (aoristic aspect), whereas the imperfect expresses progressive action (imperfective aspect). The basic usage of the aorist tense needs to be carefully observed, since it has been woefully misunderstood in the past. It has been described as having a snapshot or punctiliar kind of action, and for this reason has even been called the "lightning" tense. However, aorist verbs do not inherently portray action that happened in an instant; rather, as A.T. Robertson explains, the aorist "just treats the act as a single whole entirely irrespective of the parts or time involved" (Historical Research, 832). So in John 2:20 an aorist verb is used in speaking of how the temple "was built" in forty-six years. The action of the aorist verb is unitary or undefined (as its name denotes: "aorist" means "not determined" or "undefined").

Finally, we might say that among the Greek tenses the aorist is "the fairest of them all" (the word "aorist" rhymes with "fairest"). Or, as someone once said, Greek is an "aorist-loving language." When speaking of actions in the past tense, the Greeks preferred to use the unmarked, aoristic aspect expressed by the aorist tense. In this way they could speak in general terms about the past. This is why when verbs in other tenses appear, we should take note of how they function in stark relief against this aoristic "background."

The first aorist active indicative is made up of at least four morph slots: (1) the  augment morph, which consists of the past time morph, the epsilon augment; (2) the lexal morph, with which the definition or meaning of the word is associated, and in the first aorist will usually be the present tense stem; (3) the aspect morph, which is sa for first aorist verbs; and (4) the suffix, which will be one of the secondary active suffixes.

Observe the morph slots that constitute the following first aorist active indicative forms of  lu,w:

Notice that the 1 sg rejects the usual secondary active suffix (perhaps so as not to duplicate the 3 sg?). Otherwise, the formation of first aorist is regular.

Again, as with the imperfect tense, it is probably easier to memorize the resultant first aorist active indicative suffixes that are formed from the aspect and suffix morph slots. 

This way one does not have to "do the math," as it were, every time one encounters an aorist tense verb. Simply observe the the epsilon augment, the present tense stem, and one of the first aorist active indicative endings.

(1) The constative aorist looks at the whole of the action regardless of its extent, progress, or duration. The usage in John 2:20 regarding the building of the temple in forty-six years is a good example. See also Rom 5:14:

evbasi,leusen o` qa,natoj avpo. VAda.m me,cri Mwu?se,wj
Death reigned from Adam until Moses

(2) The ingressive aorist focuses on the initiation or commencement of an action. The shortest verse in the Bible, John 11:35 ("Jesus wept") may serve as an example of this usage:

 evda,krusen o` VIhsou/j
Jesus began to weep
(or perhaps over-dramatically) Jesus burst into tears

(3) The culminative or effective aorist views the completion or outcome of an action (or actions). English translations will often employ the present perfect tense, as in Phil 4:11:

For I have learned (e;maqon) to be content...