The simplest guide is to regard the passé composé (when it is being used to replace the passé historique) as marking the beginning (or end) of an action or state:
Pendant les 1610s. Jacques I était roi d'Angleterre. En 1625 il est mort et son fils a été roi.
(In the 1610s, Jemes I was [i.e. was being] king. In 1625 he died and his son was [i.e.became] king).I
Je voyais tous les oiseaux de ma fenêtre. (I could see all the birds from my window), mais tout d-un coup, j'ai vu une aigle. (But all of a sudden I caught sight of an eagle)
À son entrée dans l'église tout le monde chantait déjá (As he came in the church, everyone was already signing). À son entrée, tout le monde a chantè. (At the moment he came in, everyone began to sing).
Good King Wenceslas looked out... when a poor man came in sight... Did the king suddenly look out (passé composé) or was he watching all the time (imparfait). Did the poor man suddenly come into view (passé composé) or was he gradually coming into view as he got nearer (imparfait).
Je pouvais faire ça (I was able to do it all the time). J'ai pu faire ça (I suddenly had the chance to do it).
Je le savais (I knew it all along), Je l'ai su (I suddenly became aware of it).
Il pleuvait (It was raining). Le ciel est devenu noir et il a plu (the sky grew dark and the rain fell).
Il mourait tout ce jour mais il n'est mort que vers minuit. (He lay dying all that day but he did not pass away until almost midnight).
N.B. The passé composé can also be used in its original sense as a present perfect, in which case it translates exactly the English present perfect: J'ai su--I have known.
Je suis venu, j'ai vu, j'ai vaincu: I have arrived, I have looked around, I have been victorious. (which is what Caesar really meant by veni, vidi, vici). Elle est morte: she's dead.
