Petrarch's poetry can require some serious slogging to get through—take Canzone 127, the next poem in the sequence, for instance. But this particular poem is more like a walk in the park (quite literally). Once you understand about the situation with Laura, you've got the key to the matter and substance of "Chiare, fresche e dolci acque."
The way Petrarch plays with time sequences can cause a bit of a kerfuffle (yes, we said it: kerfuffle), but if you're careful about the transitions from one stanza (or strophe) to the next, you should be good. So take a look at the beginning of second stanza and beware:
If it, indeed, must be my fate, and Heaven works its ways, that Love close up these eyes while they still weep, let grace see my poor body be buried there among you (14-18)
The poet has just moved from his reverie of Laura's gorgeous body in the previous stanza to this morbid little fantasy about his potential death from lovesickness. Fast forward to the last stanza, and Petrarch reaches back into the past before returning to the present moment. Keep your eyes peeled, watch for those verb tenses and transitions—then sit back and enjoy.