A good kite will go right up. Another method is to have a friend take the kite about fifty feet downwind, and hold the kite aloft. Pull the line taut while your friend lets go of the kite. Pull the line toward you hand over hand. Play out the line as the kite gains altitude.
Kites are decidedly low tech, so problems are few.
Most problems seem centered around the need for a tail. Not all kites need a tail, but most kites can benefit from the stability offered by one in high winds. Tails can be for fun or decoration. Good quality kites will include a tail with the kite if one is needed. If the kite won't gain altitude either the wind is too feeble, the tail is too heavy, or the tow line may need to be adjusted.