Solutions
There is no single solution for any of the puzzles. A successful strategy you utilised once does not necessarily mean it will work a second time.
Experiment
Don't be afraid to experiment and try something different if you keep getting an 'Almost!', there is more than one solution to every puzzle.
Fireflies
If you need help with a stage you can make use of the fireflies for a hint by tapping on the button in the bottom right corner of the screen. You are only given a few fireflies so only use them when you are really stumped. If you run out and need more you will have to buy them through in-app purchases using real money.
New Stage
You can restart a level as many times as you want and not be penalised in any way so when you enter a new stage always have a look around and see how things work before trying to work out a solution. pay particular attention to traps and bubbles and don't forget to take into account Om Nom's transformational powers.
Spider Wizards Anti-Gravity Powers
When you encounter the candy-stealing spider wizard look for ways that you can use his anti-gravity powers which draw the candy towards him to your advantage. For example time the cutting of the rope when you know the wizards anti-gravity powers will prevent the candy from plunging into the pit below and will instead deliver it to Om Nom.
Free Gifts
When you have collected a certain amount of stars you will earn free gifts which are usually gems or more hints.
New Worlds
Although you cannot skip levels you can unlock new worlds when you have earned enough stars. If you find you are short of stars you can always replay previous levels where you did not collect all three of the stars that were available and get the required number to unlock a new world that way.