NASCAR's Competition Department distributes entry blanks for each race to owners in the series.
Those entries must be returned before the deadline, which is set 13 days in advance of the event.
When the entry is received by Competition, the car is added to the entry list.
There is an inspection fee for each entry.

If qualifying is rained out or cancelled
the teams making the race would be:
#26, Owner won a race in 2009 [Roush Daytona][36th in owners points/26 race attempts)
#09, Owner won a race in 2009 [Finch Talladega][39th in owners points/26 race attempts)
#38, 37th in 2010 Owners pts, 26 attempts
#36, 38th, 26
#13, 40th, 26
#46, 41st, 26
#87, 42nd, 26
#66, 43rd, 26
missing the race would be:
#55, 44th, 26
#64, 46th, 14

After the 5th race of the season, the current season OWNERS points are used:
#1) - First 35 by current Owner Points [team does not have to attempt all the races]
#2) - Last Years Cup Champ or the Event Champion if not already in the field
#3) - Car Owners whose team has won in the previous and current season not already in the field
#4) - Drivers who have won in the previous and current season not already in the field
#5) - Past Sprint Cup Champions not in by 1 thru 4
#6) - Qualifying Attempts with Owners points as the tie breaker
#7) - Qualifying Order Position
(all above apply as long as the team was entered by the entry deadline - usually 7-13 days before the race)

Past Champions Limited To 6 Provisional Berths in Cup: NASCAR announced an update to the past champion’s provisional rule in the Sprint Cup Series starting with the 2007 season. A past champion’s provisional may be used by an eligible driver a maximum of six times over the course of the season. In addition, a team with a past champion eligible driver may only use this provisional a maximum of six times during a season. Previously, there was no limit on usage of the past champion’s provisional over the course of the 36-race season. The provisional gives the eligible driver the 43rd and final starting position in the race field. "As NASCAR seeks to place more emphasis on competition, we have decided the time is right to limit the number of provisionals allowed,” said NASCAR Vice President of Competition Robin Pemberton. “We believe this revision brings the provisional policy in line with the continued growth of the sport.”(NASCAR PR)
This is only for a team/driver OUTSIDE the top-35 in owners points, drivers whose team is in the top-35 in owners points, would already be guaranteed in the field and not need the Past Champions Provisional
See my 2010 Past Champions Provisional Page for more.