put something in between, like in movie trailers they'll usually put a piece of dialogue just before the music changes. like that, you could also put some sort of effect between them like a glitch effect with sfx but that depends on the genre of the video
watch that tutorial. it's not teaching you how to do the exact effect you're looking for, but it teaches you stuff that will probably help you get a better idea on how to pull off the effect you specified
you say you're new to amvs, but what about software? do you have any experience at all with software to do this kind of stuff? if you don't, then a textual explanation for any of this would go way over your head--way over...like it'd be all the way in naptune or jupiter...maybe uranus.