To climb K2 from the Pakistani side, it is necessary to apply for permission from the Ministry of Tourism in Islamabad. The peak fee for south side expeditions is 7,200 USD for a team of up to 7 climbers, and 1,200 USD for each additional climber.
Permit fee for Nanga Parbat, Gasherbrum I, Broad Peak, and Gasherbrum II is 5,400 USD for a team of 7 and 900 USD for each additional climber.
In addition to the peak fee, you will need to put up a 10,000 USD rescue bond (completely refundable if it is not used), and a 68 USD environmental fee. There is a non refundable service fee of USD 300 pr team.
K2 is approximately 50 Km. from Indian boarder so you will be required to travel with a Pakistani Army "Liaison Officer" (L.O.), and each expedition would provide his allowances & equipment etc. A reasonable budget for a mid-size team (without gear) is 8,000 USD per climber. For simply trekking to Base Camp, a reasonable budget is 3,000 USD per trekker.
To climb K2 from the Chinese side, it is necessary to apply for permission from the Chinese Mountaineering Association in Beijing. The permit fee is only approximately 1,000 USD per team on this side, but the miscellaneous expenses will add up to much more. Although the total package is negotiable, the Chinese side of K2 is generally about 50% more expensive than the Pakistani side. The email address for Mr. Ying Dao Shui, Vice Secretary-General of the CMA, is firstname.lastname@example.org (allow 1-2 weeks for response).
Whichever organizer you choose, the same rules apply as for organizing a trip to Everest. You really should keep all the negotiations with the tour operator in writing. Check Permit&Paperwork on the Everest section for a list of details to be discussed closely. When arriving in Pakistan, you need to check all the gear provided (fuel bottles and such) before leaving for the trek, in order not to be up for surprises upon reaching the mountain. You won't need a Letter of Recommendation to attain a climbing permit for K2.