My kills come in a number of ways, but here's what I feel is most important:
FH B-Air:
This won't hit incredibly short characters like Kirby and Pikachu, but it'll still hit anybody who's ever so slightly tall, such as Ness, Mega Man and Villager. If they shield, it's still super safe, so it's a good option. The main problem is that B-Air doesn't kill until around 120%~ without Rage, so they'll be living for a while.
D-Tilt:
D-Tilt has a decently high trip rate. I'm not sure about the specifics, but I believe it's 30% at the base, 35% at the tip? Somebody can correct me on that. When D-Tilt trips, you can F-Smash for pretty early kills. The move puts Kirby into a crouching stance that's temporarily carried over into walking if you cancel it at the FAF with a walk, so advancing D-Tilt is a really nice option with C-Stick set to Attack. This is relatively hard to punish, although it's character dependant, mostly reliant on whether or not they can grab crouching Kirby. When combined with Perfect Pivot and Stutterstep F-Smash, your D-Tilt becomes just as important as U-Tilt. At 90%+, D-Tilt can combo into another D-Tilt if it doesn't trip, so you can get an even better chance at a F-Smash confirm. You'll need to learn your Perfect Pivots as to not miss the windows here, though.
U-Smash/D-Smash:
While both are easily punishable, remember that your U-Smash kills earlier than Fox's does, while our D-Smash covers both sides of our body. Kirby's feet are invincible during these moves, so you can use them against aerials (U-Smash) or grounded moves (D-Smash) to punish. Once you start implementing jab/inhale/ledge trump B-Air to make your ledge play terrifying, you can start getting easy kills with Smash Attacks by forcing specific get-up options.
Stone:
Using Stone to edgeguard is incredibly potent. Stone's knockback direction is dependant on what side of the opponent's hurtbox you come in contact with, so you can use this to choose to stage spike your opponent, or kill them from the blast zone. One thing that should be noted is Stone acts as a counter of sorts. For example, Kirby uses Stone to edgeguard Ryu's Side B. However, Kirby misses and rather ends up falling in front of Ryu's Side B path. Ryu's hitbox from the move will come in contact with Kirby's Stone, be tanked by the super armor, and then punished due to the hitlag that the opponent and Kirby receives. This is useful as it allows you to shove yourself straight into recoveries and ensure you'll hit them.
Inhale:
While it is incredibly gimmicky, I recommend you learn the set-ups that come with Inhale. For example, once you have somebody in your mouth, you can Jump > Copy > B-Air an unsuspecting opponent. They are allowed to move before you can, so nothing is ever confirmed, and becomes more of a guessing game. Watch what your opponent usually does after being copied and react accordingly. Along with that, I recommend you learn the best situations to go for Kirbycide. Whether you're at a percent deficit or up a stock, using Kirbycide can be deadly and put fear in the opponent. Pre-patch I'd never recommend using the technique, but it's definitely usable now. Practice your grab break techniques against certain characters so you can avoid getting footstool'd and potentially footstool them yourself.
Copy Abilities:
Learn these, they're important. Several Copy Abilities will kill the opponent, so it's good to learn the ways they can help you. Be creative with your abilities to make the most out of them and land those kills!