I find jumping and using n-special (the little blue thunderbolts) will apply a lot of pressure. Most players don't know how to react if you use them fluently. Don't spam them, but when you run toward and opponent... jump, use a thunderbolt (n-special), and follow up with an aerial.
N-air is really good for breaking strings and creating space between your opponent.
For pressure, stay close to your opponent. Pikachu has very quick attacks and come out very fast. Against Sheik or Fox, sometimes pressure or rushdowns aren't the best option. Stay safe, but attack only when it's guaranteed you'll hit the opponent.
Edit: Pikachu's u-special (Quick Attack) is also very helpful, for both escaping and attacking.
