Learn how to throw a retreating razor leaf, practice spacing, and go deep for those offstage ledge guards.
Your main method of getting kills is to get a grab, which you will get either from a read or a razor leaf punish. Down throw and up throw will combo into up-b for a kill, back throw can kill at high percents near the ledge on a lot of stages, or can set them up to be ledge guarded by your back air.
Other kill options are up-air, u-smash, down-b on floatier characters while they're high up, and at a pretty high percent. Down tilt to up-air is really good at higher percents.
For racking up damage, your nair is a a great tool. D-tilt is a amazing combo starter, and at lower damages should lead into your u-air, nair, and in some cases dair. Nair->up tilt->nair is usually a true combo at lower percents on most characters.
Covering rolls with your nair is also a heinous punish we have. Thing lasts forever, and combos into it self. Jab is also a great combo extender, it has a big hit box and comes out on frame 2, which is sooooo awesome especially when you pivot jab. It's amazing.
That should get you started.