Stairway to heaven
Up. Just, up. Up airs, man. Up. Up specials. Just, up. And not the movie.
For so many characters, combos can be string out of up tilts, up airs, and up smashes. One simple, introductory character is Mario, but many more in the roster, like Yoshi, Captain Falcon, Pikachu, Zero Suit Samus and more sport a great up air for combos.
The trick here is learning how to up tilt, short hop, up air, and fast fall reliably and with a decent amount of precision, giving you enough time to land, and then jump again to keep your juggle going.
Stages with platforms like Battlefield allow you to keep your opponent in the air while landing on platforms, moving progressively higher, and then using an up special to give opponents that final push into the blast zone.
One of the most satisfying ways to kill in Super Smash Bros. Ultimate is the spike. It's right up there with Captain Falcon's knee.
Many characters have this property on their down air, through some also have it on their forward air. The spike hits opponents and shoots them downwards - at medium to high percents this is a guaranteed kill, though at low percents it can still be used to high effect.
The main aim of this is, obviously, to get enemies off stage and use it. Good opportunities are during either low of side recoveries while edge guarding your opponent.
Though a stage spike which bounces the opponent off the platform can also lead into a jump up air combo, or even a charged smash if you've conditioned or read your opponent correctly.
The smash. A classic. Not so great for combos, but perfect for ending them. Many smashes take a while to charge up, and the shorter range attacks are going to be risky, but can be so worth it.
Just throwing out smashes when the enemy is at high percents isn't going to guarantee kills though. You need the perfect opportunity.
Get a good grasp of the range of your smash attacks, and look for unique opporunities. For example, predict an enemy's roll when they hit the floor without teching, or wait for an air dodge and punish.
Often when waiting for an enemy to recover, you can just wait on stage, following them, and anticipate an air dodge. Once it comes out, rush to where they stand and hit them with a fast smash.
Off stage intercept
While there are plenty of characters with good recoveries, there's also a fair few with pretty mediocre aerial performance. These are usually heavier characters that are harder to knock away, but they're ripe for interception to kill.
Dr. Mario is a good example. His short up special means pushing him away from the stage will kill him pretty reliably. Projectiles in the air, pushing him back ever so slightly, can ensure his death.
Low percent spikes and especially off stage footstools (jumping on an opponent's head - somewhat tricky to perform) can push enemies like Dr. Mario just low enough to ensure they'll never get back on stage.