1) Generally, long-form adjectives refer to general qualities of a subject, while short adjectives are used to describe temporary quality or condition. For example:
Он больной -- He is ill (= He has some permanent, chronic or serious illness)
Он болен -- He is ill (right how / at the moment / today etc), He is feeling unwell (eg.: Он болен и не может сегодня поехать на работу)
2) The short adjectives dont have case forms and they are almost always used as a predicate and can’t be used as an attribute:
Эта девушка очень красива (predicate) (''Эта девушка очень красивая'' is possible as well)
but:
Я вижу красивую девушку (attribute)
3) In colloquial spoken language the long adjectives are usually used