Hey! You're asking the right question. I'd love to field it, because I've thought about it a lot and I like up and coming Sheiks. I've always thought of sheik as a character who brings vicious, hard to avoid combos to get to 100% and then relies on very precise, particular methods of finishing the opponent off. Unlike many characters, most of sheik's finishers require sensitive positioning and timing, so it can feel like she doesn't have the same "guarantee" to kill up past a certain % that most characters do. However, once you get to know them, her finishers are powerful, diverse, and difficult to avoid. Their sensitivity of application is the price she pays for being the agility queen.
Here's a rough list of moves I commonly use to finish. I've given two %s: when I can often kill with them with ideal positioning, and when they kill pretty unconditionally, like from center stage; in that order. If it's more specific than that, I've noted it.
Bouncing fish (115, 160%)
Vanish (110, 140%)
Fsmash (100%, 150%)
Usmash sweetspot (100%)
Bair (100% offstage, 120% edge-of-stage, like 170% midstage)
Fair (150%-ish, varies wildly with where you hit them)
Uair (130%) (for killing opponents high in the air)
Needles (Edgeguarding tool; % mostly irrelevant)
And, situationally, with a lot of discretion, since using these correctly is hard to learn:
Grenades (150%)
Dair meteor (90%)
So those are moves to watch and pay attention to. Now, with essentially every one of these, it isn't simply a question of hitting with the moves at a certain %. Until very high %s, all of these are sensitive to where the hit lands, and in what direction. If you're interested, here's my reflections on the circumstances these moves kill best in:
Bouncing Fish:
This is my -favorite- finisher, and in general my favorite move. It starts to kill from mid-stage around 150%, but a lot of its virtue is in nailing people who are trying to get back on stage, where it can kill much closer to 100% depending on how far out the move connects. It's extremely fast, accurate, and high priority. Any time you can knock someone off the stage, a bouncing fish while they're trying to get back on might seal the deal. You'll also learn how to tag people when they create openings while they're up against the edge of a stage; it's great for leaping over projectiles and delivering a blow to ranged characters. I probably kill with this move more than any other. Make sure you get good with the manual distance control and manual timing of the kick so you're as accurate as possible with it. This move will never stop paying you back for your investment in it.
Side smash:
This is sheik's most "conventional" killer, and my second favorite lately, but it still favors heavily people close to the edge. It's one of her most dependable, low-% killers if you can push someone up to the edge of the stage with the second kick. I often try to encourage opponents to scuffle around with me close to the edge of the stage so they'll create an opening in a prime position to be side smashed.
Vanish:
This is like sheik's version of counter. It takes a longer read in advance, but pays you back by being much safer if your read is wrong, compared to other counters. What can I say except this move is great. If you can learn to use it to slip through people's moves and blow up on them, it has very high launching power and will net you a lot of sneaky kills. Learning how to reappear in judicious directions will also keep you well-guarded even when the attack misses. I encourage aiming to appear slightly off the ground rather than directly on it because it quickens your recovery time. Starting from a grounded state, the 22.5 degree angle vanish is best--but sensitive to input. The 45 degree one is worse than just reappearing on the ground, so be careful.
Usmash: This is sheik's least positioning-sensitive finisher. Up past 100% or so, anywhere on the map sheik hits with a sweet usmash will probably be a kill. Learn what situations make someone likely to be coming down on top of you without an easy time avoiding an attack. I've gotten usmash kills by throwing needles in people's face or fair-ing them and then dashing under them and usmashing, or just DCUSing under people who were trying to get their footing back from some other attack that launched them. This one's powerful, but tricky to hit with, so I would say recognize the situations where it's the right tool, but be opportunistic moreso than actively try to kill with this move.
Bair: This move's incredible and has a lot of knockback for how fast it is. A lot of its kills will be against people who are trying to get back on stage and thus already close to the blast zone. You'll find that sheik's off the edge game is very important. She has lots of agility and recovery to make sure she always gets back on safely by the time you know how to handle her, so she can afford to make risky off-the-edge plays. As for how to hit with bair against a recovering opponent, my best advice is just try it. It takes some figuring out, but you'll figure out the positionings and timings and tricks that work. Lately I've been enjoying a lot of stage spikes with this move by running off the edge and bairing an opponent making a low recovery. Also, its power is high enough that it'll easily net you kills even on grounded opponents once their % is high enough or if they're close to the edge.
Fair: Used similarly to bair, most of your fair kills will be edge guarding. This is a wonderful move but it's more comboing, maneuvering and disruption oriented than killing, so it kills at markedly lower %s. Nevertheless, its unmatched speed and precision can be good for denying recoveries and finishing foes at high %s. Also, this is probably my #1 used setup move for getting people off the stage so something like a bouncing fish can finish them off.
Uair: I get a -lot- of kills with this. It depends on hitting an opponent while they're high up, but you have a perfect tool for that in your down throw. Up past 120%, do a downthrow, jump up as high as you can, and knock them off the top of the stage. It's gorgeous. I also get a lot of people by hesitating for a second after the first jump so they air dodge, and then double jumping hitting them after the dodge. If someone just happens to be up high and you hit them with this, that'll do the trick just as fine. ftilt also does a good job putting people in the sky at high %s.
Needles: Needles have surprisingly high knockback in this game and can really push someone who's trying to recover away from the edge, or gimp a double jump. Get good at needle gliding and short hop needles/aerial needle aim in general and you'll be able to mess up quite a few recoveries. This is more situational than the rest, but valuable.
Concerning the very situational killers:
Grenades:
I never -try- to kill with grenades. But I use grenades regularly as a zoning and disruption tool and sometimes it just so happens that someone gets hit with one at the wrong time and blows up. Using grenades responsibly is a whole other can of worms. I have a thread on it in this forum.
Meteor: I -love- killing with this, but it's rare that I get to. The way you meteor smash someone with sheik is by dairing right at the edge of the stage, facing the stage. You can hit someone with the back of the attack and they'll be meteor'd if it connects right at the start. I usually roll up to the ledge so my back is to it if I'm trying to set this up. If you dair away from the edge, that is of course a suicide.
Anyway, I don't claim this list to be comprehensive, but hopefully it gets your creative juices going.