This is a Physics Game
This should be obvious, but it can be easy to forget that the central theme of this game is physics. You are trying to get these little Gooballs to make the buildings you need. They are limited by the games physics though. If your tower is swaying badly, then you need to fix that before you go any further. Remember to keep the weight fairly balanced on both sides. Once it starts swaying, it is really hard to stop it without using a time bug.
You should also learn to balance your goals well. Most levels challenge you to make a strong structure with the least Goo possible. This is challenging, since the most effective way to do this is usually to make a narrow tower. Narrow towers are the least stable though. Figure out a good blend between the two strategies. A good setup is usually to have about 5 or 6 Gooballs forming a strong square base.
If you are building a big tower or bridge, remember to use anchor points. These are just simple extensions from your main structure that rest on something firm. My personal favorite is to have a Gooball on each side of my tower's base. Then it forms a triangle that presses against the ground if it starts to sway.
Timebugs are Your Friends
Don't forget about the timebugs. These little white insects are your best friend for the times when you mess up your grand plan. Put a Gooball in the wrong place? Just click a timebug to go back a step. If your tower falls over completely, you can use a few timebugs to try and make some emergency repairs in time.
There are a number of levels where you just need to build as fast as possible. I'm not just talking about the ones with a time limit either. Some structures tend to destabilize the longer you wait. Towers seem to sway more as the Gooballs climb and shift their weight. This can easily wreck your tower. On the other hand, bridges usually stop swaying over time. This can be disastrous when you are trying to catch onto an anchor point on the other side. That sway might just have given you enough height to latch onto the other side.
The Power of the Pipe
Another reason to build quickly is that the pipe's suction is quite strong. It is effectively another anchor point for your structure once you are within range. Your unstable tower is going to be just fine as long as you reach that pipe before it falls apart.
Don’t Forget Your Greens
If you are trying to get an OCD flag on a level or if you want to collect more Gooballs for the World of Goo Corporation Challenge, then you can't forget about the green Gooballs. These Gooballs are afraid of commitment (according to the game's dry humor). They can be reused in your structure. This also means that they can be freed. Once you get to the pipe in a level, you should try to deconstruct the tower. Just pull the greens off and let them climb up the structure to the pipe. It's possible to leave only one Gooball behind, since the green Gooballs can often hang on as just a free chain dangling from the pipe. It can be the difference between a normal finish and an OCD flag.
Take a Good Look
Most levels in World of Goo are fairly easy to figure out once you really take a look at them. Take a minute to scan the entire level before you commit to a single structure. Look for any unique obstacles or features that might be important to your goal. Remember, if there is a time limit for the OCD goal, you can always restart later.
Signpost are another important aspect of this search. These cryptic messages are usually good clues as to just what you are supposed to do in a level.
Be Happy When You Fail
You are going to fail a lot. That's just the truth. Just take it in stride and enjoy the spectacle of your tower's collapse. Then restart the level with the knowledge that Plan A won't work. Most of the missions past chapter 2 will practically demand that you fail once, just to figure out the level's unique dynamic. The truth is that you are usually better off if you just go with your gut and try the first crazy thing that comes to your mind. The levels are intuitive, so you won't be wrong too often.
If worse comes to worse, you can always skip the levels through the menu. You might be better prepared after you've played a bit more.
Forget OCD Mode…For Now
This is for your own good. If you are having trouble with the puzzles already, you are not going to have fun in OCD mode. A number of OCD challenges require that you complete the puzzle perfectly. Not good or excellent, perfect. If you mess up one Gooball placement, this can cost you your OCD title. Don't drive yourself crazy trying to meet the challenges. They are there for an extra boost at the end of the game. Finish all the levels and then come back to get your OCD flags.