'Cool'  or 'coolness' is very difficult to define. I originally wanted to explain 'cool' using my own thoughts; although I immediately struggled to describe the status of cool.  I generally do not like to directly quote Wikipedia, as it is a lazy cop-out and quite possibly inaccurate; although I found that the Wikipedia definition of 'coolness' seemed to cover the basics for this post anyway...

Cool (aesthetic) From Wikipedia, the free encyclopedia

'Something regarded as cool is an admired aesthetic of attitude, behavior, comportment, appearance and style, influenced by and a product of the Zeitgeist. Because of the varied and changing connotations of cool, as well its subjective nature, the word has no single meaning. It has associations of composure and self-control and often is used as an expression of admiration or approval. Although commonly regarded as slang, it is widely used among disparate social groups, and has endured in usage for generations.'

I should advise you check the whole artical on Wikipedia - Cool (aesthetic)

Many people, mostly aged between 20 and 45 (I am outside this catagory now), desperately wish to attain the status of cool. It may take them a long time to reach the goal of natural coolness, which is the point when they no longer need to try. They will spend a lot of their income on staying one step ahead of the current fashions. They will need to be seen in the most happening locations; be seen with the right people and discussing the important cool 'stuff'. I believe going to certain colleges and dropping out of particular art courses is also very important.  Of couse, being seen at the coolest clubs is a good thing; but still being seen there when that club has become popular is a bad thing. It is also quite possible to be cool when living in another country, which allows for the obliviousness of common styles and culture, thus realizing a particular self confidence in persona. This is particularly true in the music and fashion centre capitals of the world.

Eventually, a young man will attain the perfect status of cool. At this point he will not even realise he is cool. He will just 'be'. He will not need to think about fashion and music, or people and places.  He will just do all these things without any inner thought.  A form of zen cool.

For any normal person, a simple thing like leaning against a tree in a public place, may seem like a simple matter (even though it may feel somewhat awkward or embarrassing). Why would we need to lean against a tree in the first place?  A cool person would use the act of leaning against a tree for two main purposes: being seen by members of the public, and watching out for other cool people.

The location should be a popular public place with a mixture of general public and cool people. The London Southbank is a good example of this, with a large and varied demographic of pedestrian public. Many will have cameras, which will ensure being photographed while leaning against a tree.

The tree itself should be chosen carefully. A very large and mature tree may render the person less important and proportionally insignificant in size. A very small tree would be quite unsuitable, as it may not support the person safely.  The tree should also be chosen for its aesthetic appeal; for example a tree with a very cool silver camouflage style bark.

An individual fashion style is intrinsic to the whole act of leaning against a tree. I could not possibly advise on the fashion elements of the process.  I believe it would help if it was a good combination of designs resulting in a relaxed and unpretentious look. 

The stance is possibly the most important point, even if all the other points have been covered. There are many styles of leaning thoughout the history of coolness, which all have their particular good points, although a truly cool person must find his own way of leaning.  The turn of the face, the expression and composure, the angle of lean are all important; but very often it is the finishing touches which complete the whole image...  the position of hands and fingers.

I present to you the cool method of leaning against a tree.