For English-speaking students of Russian, I've written a short dialogue for another language blog with usage examples for several of the "modal" Russian verbs discussed in this thread:
Maria, Carlos, and Lola
Mostly the verbs are in the present tense, because the primary emphasis is on the difference between positive and negated modal constructions, such as:
Тебе надо позвонить Карлосу.
You have to call Carlos.
Тебе не надо звонить Карлосу.
You shouldn't call Carlos.
Ты можешь не звонить Карлосу.
You don't have to call Carlos (if you'd rather not).
Ты не можешь звонить Карлосу.
You cannot call Carlos (because I threw your cellphone into the aquarium).
Thus, I didn't really get deeply into a discussion of tense or aspect.
I would repost the whole thing here, but technically it's work-for-hire under copyright to the other blog. Anyway, I hope it's a useful summary for students, and I would certainly welcome comments from native Russians if there are problems with the phrasings I use.