Origami is generally fiddly, difficult to describe without diagrams, and prone to small early errors leading to large later difficulties. Paper planes in particular are very sensitive to just the right folds in the right places to stop them corkscrewing into the floor as soon as you let them go.
The following paper plane is the exception to all the above rules. It is very, very easy to make, and reasonably easy to describe. It's actually difficult to make it badly, and almost any effort will fly acceptably.
What You Need to Start
To start, you need a square of paper, preferably about 200mm along each side. If the only piece of paper you have is rectangular instead of square - A4 say - don't worry, you can soon make a good enough square from that. If you don't have a piece of paper at all, go and get one - this is really easy and worth doing.
To make a square, simply fold down one corner of the rectangle until the whole of a short edge is lying along one of the long edges. The crease should go to the corner and make an angle of 45 degrees. You've now got a square, folded in half along its diagonal, with a little rectangle attached to one edge. Cut or tear along that edge to leave a square.
If You've Got a Square Already
So, now you have a square. If it doesn't already have a single diagonal fold, give it one.
Now, place the paper on a flat surface with that diagonal fold lying horizontally, as though you were about to use it as a guide to write along. Lay the paper down so that the fold is a 'valley' rather than a 'mountain' fold. Now take the corner of the square that is nearest to you, and fold it over towards the centre. Move it only about 20mm towards the centre, then make a crease. Now fold it over again, the same distance, and keep repeating this until you reach the centre. When you reach the centre you should have a right-angled isosceles triangle with a very thick base. When you have this, repeat the fold over once more so that the base of the triangle has two small triangular flaps sticking out.
Now, keeping the centre of the base of the triangle on the table, bring the two flaps up to meet each other. You should find you can tuck one into the other quite firmly, making a circle. The object you are left with looks a little like a bishop's mitre, and nothing at all like a paper aeroplane.
The Moment of Truth
Hold the plane gently by the ring. The main 'wing' should be at the bottom of the ring and should point back - the ring is the leading edge. Hold the plane high above your head and move it forward gently and release. Do not throw it hard - flow over the wing breaks down and it won't fly. It should coast in a fairly straight line to a landing a good deal further away than you thought. Enterprising students will notice that the glide angle is pretty close to the angle of many lecture theatres...
How Does it Work?
The area of paper plane aerodynamics is a complex and still evolving field, and a complete explanation of the principles involved are beyond the scope of the entry. However, this Researcher has been reliably informed that this design uses a phenomenon known as compression lift to achieve its remarkably stable flight. It is not known at this time whether any full-scale designs have been produced using this phenomenon.