Little knowledge drop:
Waveshine -> attack/grab works on:
Bowser, Samus, Sheik, Zelda, Peach, Link, Captain Falcon, Ganondorf, Donkey Kong, Yoshi, King Dedede, Lucario, Wario, Charizard, ROB, Snake, Olimar, Ike
Characters that fall down from it (techchase those):
Fox, Falco, Kirby, Pikachu, Mewtwo, Jiggypuff, Roy, Toon Link, Game and Watch, Meta Knight, Pit, Lucas, Sonic, Zero Suit Samus, Ivysaur, Diddy Kong, Wolf, Squirtle
Note that characters with high traction values will only slide a bit when falling down (Jiggs, MK) while low traction values will make them slide more (Roy, Squirtle) so the techchase becomes less likely, but you get normally a zoning advantage with it and you can use their bad stage position.
These characters will not fall from shine and have to low traction values to get a followup:
Mario, Marth, Ice Climbers, Ness, Luigi
Either try to use your remaining frame advantage to bait them into stuff and punish, use their zoning/centerstage advantage or try catching bad DI with perfect waveshine (remember to dash ASAP) into a quick move like another shine or dash attack. If you have bigger frame windows, use more optimal choices like grab, up-tilt or up-smash or aerials depending on the situation.
Little note if you want to be a tech skill beast: You can also get waveshines on "standard" DIs on the last category if you shine->jump&press forward->perfect distance WD->dash on frame 11 after your WD input (if you press it too early it buffers and you will only walk)->dash until you reached them->if you are in run animation, run-cancel (press down)->shine, if you are in initial dash still, pivot shine (press as if you would walk, not run, in the opposing direction for one frame and immediately shine). Fox exits initial dash and enters run animation on frame 15 of his dash.
Also a low-priority tech skill optimization.
Regarding the multishine topic, I wouldn't try to learn it, at least not as high priority aim. Try to be able to do doubleshines consistently though, those are worth something.
One basic mindgame you can optimize with it is if you shine a shield: Shinegrab is one main option, but they might shine in the time you grab, so in this case the doubleshine hits them in their jumpsquat (before they can shine). The opponent also has the option to keep shielding, and if you doubleshine their shield and are not on the ground afterwards, that is a problem, while if you can do doubleshines, you can doubleshine->WD back or doubleshine->grab.
Basically, if you hit a shield with a shine, WD, grab or do an aerial, with optinally doing a second shine before.
It also helps if you shine a light character and read the tech/no-tech, then shine->wait a little moment->shinegrab will probably work, sometimes also shine-up-smash.
If you do a run-cancel shine in general, you still have a decent amount of momentum, so a shinegrab will normally work, both the shine and the grab will hit (on characters that don't fall down from it). Same goes for shine->up-smash without an inbetween WD. If you don't do the shine out of high velocity, the shine will knock them too far away to get the next hit, so waveshine in this case.
Waveshines are your main tool though.
Regarding shine spikes, basically it is just hitting them. If you are opposed to another hitbox, try to aim with an angle at which your hurtbox is farer away so you won't get hit before you can shine. It is mainly practice. One thing, really good players, will SDI up to get sent less down. Some top Fox players prepare for this case, by jumping out and doing dair or bair ASAP. Only do that if you know your opponent SDIs the shinespike up and it doesn't risk you, because it isn't worth it if there is a high chance of SDing going within it.
Regarding on how to physically do the button inputs, it is just practice, if it helps you, try different methods. I for my part like to play with the PM-modified claw which really helps with difficult tech skill, but the most important thing is that it works for you.