I felt I should've given it a little bit more elaboration, so I'm going to try to explain it to you now.
From what little you've read, an Assist Technique is essentially an attack performed by one of the playable characters that is unique to his moveset.
A good(and currently the only example) is on the Silver Hood sheet.
The Assist Character is chosen as the Vs. Mode panel, and you can choose from any of the 16 characters. This is pending to change, depending on the popularity of the game, as if we get more good and acceptable characters then the roster can handle, then We'll expand it so you can also choose from a small list of non-playable character cameos.
But for the time being, you can only choose from playable ppls. If you choose Silver Hood, he'll appear onstage, force some of the metal on his mask to attack your opponent, then leave. Seems simple enough.
So, you're probably wondering what factors you should think about when choosing an assist character. Well, seeing as how they get one attack big or otherwise, it isn't tough to make a choice. But there is one thing, the projectiles system is disabled with Assists, meaning that any projectiles that you or the assist shoot will always aim for the middle. That's the only real thing you should keep in mind, though.
I hope that helps some of you a little.