Could anyone refer me to a rule explaining why verbs ending with -ere have different stressed syllables? What I have understood so far is that I should look them up in the dictionary.
Conventionally, people say that Italian verbs fall into three categories, or conjugations: those ending in -are, in -ere and in -ire. Those in -ere, however, correspond to two different conjugations in Latin (where there were four conjugations for verbs):
So, about your examples, tenere derives from tenēre (first person teneo, which is how you'll find it in a Latin vocabulary); and the analogous holds for verbs such as dovere, godere, persuadere, vedere, the derivates of tenere (such as trattenere, mantenere, contenere and so on) etc.
On the other hand, prendere derives from prehendĕre (prehendo), and an analogous stress is found in other verbs from Latin third conjugation, such as giungere, leggere, tendere, vincere and many more.
I am afraid this is not of much help unless one knows well one's Latin, and moreover there are exceptions: verbs that have modified their stress with respect to their Latin ancestor, such as Italian rìdere, from Latin ridēre, mòrdere from mordēre and so on.