How do you fall through platforms in Super Smash Bros (N64)?

Solution 1:

After you finish an up B move and enter the "helpless" falling state, you can fall through soft platforms by simply holding down on the joystick. This state is the only time you can fall through a platform as if it were not there.

Not all characters can do this. Examples include Kirby (the final down-stroke of his final cutter up B does not ever finish until interrupted by landing/getting hit/blast zone) as well as both Jigglypuff and Yoshi (the two non-jumping up B's). Also Falcon's up B does not make him helpless if it connects with an opponent (but does remove his second (aerial) jump). A related special case is Fox's up B (the fire fox) can also pass through soft platforms during the move itself, when aimed downwards.

In all other cases, you can't fall through a platform per se, so it must be done in two steps: land, then drop through. Given enough practice with the timing, it is possible to perform the two step sequence fluidly and almost seamlessly. The fastest way to drop through a platform from a standing state is to "shield drop" by pressing Z and down on the stick at the same time. It saves a frame or two of ducking animation compared to the normal smash the stick downwards method, and also works while running/dashing.

Solution 2:

It's all in the timing, you have to double tap down as you're about to hit the platform and you'll land on the platform below.

Solution 3:

I'm not 100% sure, it's been a while since I played an N64, but if you are on a platform and pass through it and if you hold down you will just continue through lower soft platforms.