Kite flying has been pursued for centuries, accredited to China, but many areas have put their stamp on it, be it the multi-cell dragon kites of China, the massive kites of Guatemala, small fighter kites of India and other areas within Asia (where the line is more important than the kite itself), musical kites bearing flutes in Vietnam, to the modern inflatable kites seen at kite festivals around the world.
Kite flying in the UK has been seen as a children's activity but sadly many experiences are blighted by the wrong conditions, incorrect assembly or impatience. Most kites operate within a wind range: too light and it cannot get enough lift for the weight, too strong and the kite can deform creating instability. The range varies for each kite; if buying a kite, the packaging should normally indicate the required wind range for operation. Beyond that the tips are to ensure that the dihedral - typically a plastic 'V' shaped component that fits to the centre spine and has holes to attach the horizontals spars - (if there is one) is the right way round - the kite sail should sweep backwards with the wind - affix the tails, if part of the design, and let out a good length of line; kites do not fly well if the line is too short, and of course ensure that the wind is blowing onto your back and then to the kite. Having said that, safety precautions obviously indicate that the kite should be well away from overhead power lines or obstrctions, be well clear of roads and people (in case it should come down across the road or into a group of people).
The best way to see the variety of kites and skills of flying is to visit a kite festival, as organisers will seek to present a cross-section of flyers and kites. In the UK, most festivals take place between May and September, typically across a weekend.