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:
#09, Owner won a race in 2009 [Finch Talladega][45th in owners points/4 race attempts)
#71 Past Champion - 2000 BLabonte [30th, 4]
#82, 12th in 2010 Owners pts, 4 attempts
#36, 35th, 4
#13, 39th, 4
#55, 41st, 4
#66, 42nd, 4
#87, 43rd, 4
missing the race would be:
#90, 44th, 4
#46, 47th, 4

Top-35 in Owner Points and guaranteed a starting spot at Bristol Motor Speedway [on March 21st] and first five races of 2010 [Bristol is the 5th and final race using 2009 owners points]:
Teams that are guaranteed a starting spot for the first five races, but are currently out of the 2010 top 35 of owners points are:
36) #37-Conway/Front Row: 0 points out of 35th
37) #26-Said/Latitude 43: -24
38) #7-Gordon/RGM: -27
Three teams are currently outside the 2009 Top 35 owners points and a guaranteed starting spot, but are in the top 35 for 2010 owners points after four races, which would assure a starting spot if qualifying at Bristol Motor Speedway is canceled [rain out, etc]:
#82-Speed/Red Bull: 12th in 2010 Owners Points
#71-Labonte/TRG: 30th, but would get in via being a past champ anyway
#36-Bliss/Baldwin: 35th in 2010 Owners Points
#09-Almirola/Phoenix Racing missed the race at Atlanta, is 45th but would make the race via being a past winning team in 2009 [winning at Talladega last April]
The other teams likely to attempt Bristol on March 21st that would make the race if qualifying is canceled would be (5):
#13-Papis (39th in 2010 owners points); #55-McDowell (41st); #66-Blaney (42nd) and #87-Nemechek (43rd). Missing the race would be: #90-Mears (44th) and #46-Cook (47th)
For the owners points standings, see my 2010 Owners Points Standings and 2010 Owners Points Rack for the first five races.(3-7-2010)

What happens if qualifying gets rained out?
If it is the first 5 races of the season, the previous season OWNERS points are used:
#1) - Previous season Owner Points [position 1-35][team does not have to attempt all the races]
#2) - Race winners from the previous and current season not already in the field
#3) - Past Sprint Cup Champions not in by 1 or 2
#4) - Current season Owner Points [Top 35][not in by rules 1-3]
#5) - Current season race attempts ties broken by current owners points standings [not in by rules 1-4]

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 2009 Past Champions Provisional Page for more.