Here you can find the whole explanation, for every case: http://www.hebrew4christians.com/Grammar/Unit_Four/Conjunctive_Vav/conjunctive_vav.html

Good to know, Yaron. Toda. What triggered the question is that I rarely see/hear the Vav pronounced as anything other than "ve" in the various Hebrew learning resources I've encountered -- pretty much only in liturgy -- but I did see a YouTube video going over vocabulary that pronounced the vav as "u". I'd previously thought it was primarily a liturgy/ancient Hebrew thing before that.

Even though they have already answered your question I just wanna add that you really shouldn't focus on that gramar rule. Most Israelies even don't know it that well and just say "ve" all the time . Hebrew grammar can be confusing at times and this is definitely not a grammar rule you should be breaking your tounge on.