I have been drilling myself in "Ancient Greek basic vocabulary" over at memrise, and I find that my biggest difficulty with learning a word is remembering where the accent is. It's not that hard for me to remember that 'daughter' is θυγατηρ, except that I've had trouble with whether the accent is on the ultima or the penult. (I know it can't be on the antepenult because the ultima is long). I'm just focusing on the basic forms - the dictionary entries. I know that accents frequently change when the word is declined. I'll worry about that later.
I've been trying to find better mnemonics. For instance, if I can remember how "divine" is accented I can think of "divine daughter" θεία θυγάτηρ, both of whom are accented on the penult. (I know it is θεία and not θεῖα because it is a 1st declension noun, and so has a long -α. The circumflex can appear only a long penult if the ultima is short.) I think "divine" is a good choice because "mortal" βροτός is accented on the last syllable.
Now I had thought that Greek words were basically those accented on the last syllable and those that were recessive, but it turns out there are words like αὐτίκα that have a short -α and thus *could* have an accented antepenult, but don't. So I can't quite divide words into "divine" and "mortal" without leaving out some words.
It would be nice to know some more general rules. I've learned that verbs are recessive (the accent is as far forward as possible, which for -ω verbs means the penult), but I'm at a loss for more comprehensive rules. Anyone know of any? Even rules that only work 90% of the time would be fine, since I could then just try to learn the exceptions.