Utilt combos into itself several times from 0%, and after that you can then followup from it into aerials (uair, nair, bair). Uair can often combo into another aerial at low %s too. Basically, the first 30-40% of an opponent's stock can be taken if you get an up tilt off.
Landing in the middle of your fair can allow you to combo into a lot of stuff, and is especially good for setting up that low % up tilt, which you should be hunting for when they come back on a new stock.
To give an example, an easy and staple combo from 0% is something like fastfall fair > up tiltx3-5 (depending on opponent's fall speed) > aerial(s) of choice. Easy 0-30% on most characters and potentially more against fastfallers. Just don't overly use fastfall forward air approach; the potential reward from it at low %s is high, but it's not safe on shield. You can mix it up with tomahawk grabs (act like you're going to fair but then just empty land and grab their shield instead).
Speaking of grabs, you can use down throw to combo into aerials at low %s. Forward throw > dash attack can also work at 0% as a mixup if they aren't expecting it. Up throw > Thunder can combo if they don't DI left/right, and is usually the best thing to try for once your opponent's % is too high for down throw to combo anymore.
Down tilt leads to grabs and sometimes trips them up for you, too. Yay. Really good move as it has basically no end lag, making it hard to punish. Make sure you make good use of it!
One other thing Pikachu is really good at that's a bit overlooked is jab resets. These are good because you can convert a knockdown from a relatively safe quick move into a lot of damage and potentially a kill. The two main setups I use are:
Shorthop neutral air at 50% > fall forward with and land in front of opponent > jab (x3) > partly charged forward smash.
Down tilt at 85% > run forward > jab (x3) > partly charged forward smash. This one has a good shot at killing lighter characters.
You have a bit of time to spare between each jab, so do it calmly and use the jabs to position yourself and your opponent so that you can hit with the strongest part of forward smash (the middle) as they get up.
If playing customs, substitute the fsmash off a jab reset for a partly charged Heavy Skull Bash. It has much more knockback and damage than forward smash.
Here's an example of the down tilt setup, using Heavy Skull Bash as the finisher rather than forward smash.
Pikachu has tons of combos, so it should come pretty naturally once you're used to him.