The foremost important thing about paper airplane construction is how you fold the plane you're making. Making creases in paper can be a very hard task that requires varying degrees of pressure. For the most part you will try to fold a flat crease when folding at the wings and fuselage. This is not always the case, but the majority of the time it will be. A good way to ensure the folds are as flat as possible is to use the tip of your finger to flatten out the crease. Unless otherwise directed, avoid using your fingernails (which may scratch or rip the paper) and do not apply too much pressure
Symmetry is important when folding. Except for the nose and fuselage, the major parts of the plane are usually made in pairs. That means that you need to make the major parts of the plane exactly the same. Very few paper airplanes successfully fly with an non-symmetrical setup. Non-symmetrical paper airplanes can fly although the flights will be skewed. When folding wings, it is important to ensure they are both the same size. The same goes for tailplanes, canards or anhedrals/dihedrals if they are folded. It is also important that their angles match, a fold should not be angled up or out while the other is down or in.