Ok, so you want to do a private trip.  Perhaps you are a skilled boatman or you know someone who is.  For starters, you will need a permit from the National Park Service (NPS).  To get the permit, you must win the NPS "lottery".  Here's the skinny.

1.  You must first apply for a permit from the National Park Service.  Each year in February, a main lottery is held to assigned launch dates for river trips occuring the next year.  You can only apply in February and must apply before the cut-off date.  Follow-up lotteries are then held as needed throughout the remainder of the year to reassign cancelled and / or leftover river trips.  The drawing for permits for 2011 was on Feb. 26, 2010.   These permits were for 12-25 day trips (longer trips available in winter).  There were follow-up lotteries for cancelled trips held in April, May and June (of 2010).

2.  The application fee is $25 (non-refundable).  Applicants who win through the lottery are charged an additional $400 (non-refundable) within 1-5 days of winning.  This fee is applied toward your permits. Each lottery applicant can list five dates.  If you win the lottery, your dates will be checked and you will be awarded the first one available on your list.  You can apply for either a standard size (1-16 people) or a small size (1-8 people) trip.  

3.  This is a "weighted" lottery which means that you, as the applicant will get more chances of winning if you have not been down the Grand Canyon in the last five years.  This includes travel on either commercial or non-commercial trips.  If it has been 5 years or more, you get 5 chances.  If you went on a commercial trip last year, you get only one chance.  If your potential alternate trip leader(s) qualifies for fewer points than you, you will be awarded the smaller number of chances.  It is best to list at least two PATLs on your application and, ideally, everyone qualifies for 5 chances (you will then get five).  Your total chance of winning in a lottery will depend both on your applications total chances and on the chances of all those who apply for the same dates as you.  For more detail, read the faqs pdf listed below.

4.  You will have a much better chance to win an out of season date (like in January rather than in June) as fewer people apply for these dates.

5.  If you choose to put together a motorized noncommercial trip, dates are limited to April 1 - Sept. 15, the trip cannot be more than 12 days (11 nights), and you must use a four stroke outboard motor .

6.  If you win, you must then put your trip together.  This includes permits, rafts, transportation to and from the take-in / take-out, food, groovers (toilets), water purification, first aid, tents, sleeping bags, and the list can go on and on.  One excellent solution is to contact an outfitter like pro or ceiba and have them pretty much take care of completely outfitting your trip for you.   Typical quote for 16 people in 5 rafts for 16 days is about $14,000.  For more support companies, see this link.

Here are some useful links from the NPS for private trip info

FAQs regarding the lottery (pdf)   Read this completely before submitting your application.  Pay special attention to the info on page 6 regarding PATLs (potential alternate trip leaders or co-applicant) before signing up

12-25 day non-commercial trip information  Includes a link to sign up for the weighted lottery, and a pdf covering noncommercial river trip regulations

The weighted lottery very useful information

Statistics from previous years regarding lottery winners.

Noncommercial River Trip Regulations (especially read page 14)