Hey again. Another question that just popped up: how do I know which aorist stem I shall use? How do I for example now that παιδεύω becomes ἐπαίδευσα and not something like ἐπιδυον. Hope my question was understandable. Take care.
When it comes down to it, you just to learn it for each verb – but it’s not as bad as it could be because there are general patterns, like with your example, -εύω > -ευσα almost always, but also -έω > -ησα, -άω > -ησα, -όω > -ωσα, -ιζω > -ισα, -άζω > -ασα, -αίνω > -ανα. Your textbook should hopefully mention these somewhere. But there are exceptions to many of them, I can think of καλέω > ἐκάλεσα, γελάω > ἐγέλασα, κράζω > ἔκραξα, μαθαίνω > ἔμαθον. And the more common a word is, the more likely it is to be irregular. I think it’s a matter of being exposed to the forms enough times and then you get a feeling for what sounds right and what sounds wrong.
Unfortunately, you have to memorize it. The reason the aorist is listed separately from the present is because it uses a different stem which can’t be consistently derived from the present.
There are some patterns, however:
Verbs with a vowel stem in the present most frequently add a simple σ- to form the aorist.
Liquid stems (λ,μ,ν,ρ) lengthen their vowel instead of adding a σ. (στελλω → εστειλα; κρινω → εκρινα)
Stops show consonant mutation. π,β,φ + σ → ψ ; κ,γ,χ + σ → ξ. Examples: πεμπω → επεμψα; γραφω → εγραψα; λεγω → ελεξα
Verbs which have a second aorist (as λειπω ελιπον) usually use a shorter (and often noticably different) stem than the present. I’m not sure if there’s a way to predict which verbs have a second aorist simply from their form in the present; I tend to doubt it.
Going the other way, maybe you could say that in general if they don’t have -ε- in the present stem or if they have a suffix, then they don’t have second aorists? There are a lot of exceptions that I can think of right away, λαμβάνω, μαθαίνω, ἄγω, βάλλω, ἁμαρτάνω, so I don’t know if such a rule of thumb would be of any use.
Thanks again guys.
I don’t think it says anywhere in my textbooks. We basically just use an anthology with some extracts from famous writers and a wordlist and some comments to it, plus that grammar book which I find quite hard to get something out of.
My teacher has a very practical approach to the language. It’s more like memorize this and that and don’t ask or think about why it is like that, it just is. I believe this is a very economic and efficient way but sometimes I just can’t hold my questions. 
I have just started my course at the university and I get the feeling that I’m going to post quite a few topics here hehe. But well, we’re going forward at a pretty high pace so hopefully I will be able to answer some lost greek students in the future.
You might be interested in reading up on the (pre)history of Greek and its Indo-European roots, because there’s where you’ll probably find the most satisfying answers to “why” questions, since things at least appear more regular when you look at the etymological roots. E.g. if you take spiphany’s example of στέλλω / ἔστειλα, it doesn’t form the aorist using -σ-, but it goes back to forms that do, because originally the present was στέλ-yω and the aorist ἔ-στελ-σα and through regular sound changes you get the forms you see in your textbook. Although I find this interesting, it’s never helped me in learning forms, but it does for some people, and it’s a decent answer to “why” questions, so you might be interested in this sort of thing.
Banana tree, where are you located? You might find Adolph Kaegi’s Short Grammar of Classical Greek helpful. (Or if you read German, Kurzgefasste griechische Schulgrammatik). It’s in print in the US, as well as available as a free electronic text through various sources (check archive.org).
I like it because it’s fairly concise (MUCH easier to find information than in Smyth) and does cover things like consonant mutation and typical patterns for verbs, which help find some underlying order in what often seems to be a chaotic and bewildering variety of forms. He doesn’t systematically discuss the historical development of the language, but when a contraction or other phonetic change has taken place, he often will have a note about it.