Here's a few tips:
1.Jigglypuff, despite common perception, has quite a lot of kill potential:
Rest(very, very powerful, but very, very hard to hit with)
Fsmash
Usmash
Fair(best kill move right here)
Utilt
Dash attack
Rollout
2. Unfortunately, despite having kill potential, her ground moves are kinda the worst in the game. Just about every single one of her ground moves lacks range, priority, speed, strength, or an unfortunate combination of the four.
3. However, that doesn't mean her ground game is completely useless. Fsmash and Usmash are a bit laggy and have small hitboxes, but they can kill and punish well if you time them correctly. Rollout can also be an excellent punisher, and utilt has good kill and combo potential as well. Also, her dash attack is quick and has nice kill power.
(Don't ever use dsmash or dtilt. They're bloody useless.)
4. Jigglypuff actually has a REALLY good grab game. Her grab itself has very good range and speed, her pummel does 3%, and each of her throws do 10-11%. Utilize this a lot.
5. As Jigglypuff, you'll be spending most of your time in the air to compensate for your ground game. Use bair and dair for spacing,approaching, and racking up damage. NEVER use fair as a regular attack- it stales really easily and you need it for killing. Use bair or nair instead. Finally, as for uair, use it for hitting enemies above you.
6. As for her specials...
Pound (her side-b) is arguably her best move. It offers infinite horizontal recovery in addition to her six jumps, has a big, enduring hitbox, and TONS of priority. You can even use it for kills in the air, since it sends enemies straight upward.
Rest (down-b) has loads of kill power, and ranks right up there with reverse falcon punches as one of the most satisfying moves in the game to land.

The hitbox is her body, so you literally need to be in the opponent to land it. The best way to do this is to use dair on the ground and rest when you land in them.
Sing (up-b) is utterly useless. Use it as a taunt.
Rollout(good ol' neutral B) has lots of kill power, but requires you to charge it up. It's pretty easy to anticipate and punish as an opponent, so the best use for it would be to punish landings.
7. Jiggs is, tragically, the lightest character in the game. Practice DIing and SDIing. A lot.
Hope this helps. :D