The main spanners in the works are the very common words with a surplus -e:
have, give, live, gone, are
against
gave, drive, alive, bone, care.
The basic idea is that when a, e, i, o and u are followed by a single consonant and another vowel, they are open and have a long sound:
came, theme, time, tome, tune.
When they are closed, i.e. followed by just one or more consonants (at hand, in print, on cost, up under) or several consonants and a vowel (banter, hinder, under, batter, bitter, hotter, butter), they have a short sound.
That is the main way of spelling a, i and u as long and short vowels.
Long e or /ee/ has only 86 words with that method (here, eve, even...).
Long o has lots of exceptions too (roll, coal, bowl).
It often does not work for reading either.