Kundalini is a deposit of spiritual energy at the base of the spine.
Some say that it is related to sexual performance, and that during the orgasm, some of the energy is wasted. This is one of the reasons sexual continence is important in some schools of Yoga, to preserve the energy.
When the coil is awakened, the spiritual alchemist will most likely guide the connection up to the sahasrara chakra, otherwise known as the crown chakra or thousand-petalled lotus. The coil will complete the circuit within the body, making one have a constant current of energy through oneself.
It is not uncommon for the awakener to realise great abilities after this event. They will probably also get a big headswell. This is why discipline is so important. One must learn to control one's greed and lust, otherwise it will result in foul action (karma), further resulting in foul reaction, possibly crushing the practicioner. (Trust me on this one, I know from experience)
As for methods for the actual awakening, some say moving down the prana (energy of breath, upward energy) and moving up the apana (energy of excreta, downward energy) will bring about this event. Selfless devotion would be a good way to go; focus on the goal would be necessary.
If not, try saying this incantation with intent, while making the kundalini be sucked up toward your head:
Wake up Mother Kundalini.
Thou whose nature is Bliss Eternal -
The Bliss of Brahman.
Thou dwelling like a serpent asleep at the lotus of Muladhara,
Sore, affected and distressed am I in body and mind,
Do thou bless me and leave thy place at the basic lotus.
Consort of Siva the Self-caused Lord of Universe,
Do thou take thy upward course through the central canal.
Leaving behind Svadhishthana,
Manipuraka, Anahata, Vishuddha, and Ajna.
Be thou united with Siva, thy Lord the God.
At Sahasrara - the thousand-petalled-lotus in the brain.
Sport there freely, O Mother,
Giver of Bliss Supreme.
Mother, who is Existence, Knowledge, Bliss Absolute.
Wake up, Mother Kundalini!
- Swami Sivananda