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.

What happens if all qualifying gets cancelled [rain/weather/other]?
If bad weather cancels qualifying, the final starting lineup will be determined by practice speeds. The same rule book procedures will be used to determine eligibility to start a race. If weather cancels practice sessions, then the starting lineup will be set by points, per the rule book.
IF QUALIFYING AND ALL PRACTICES ARE CANCELED, then:
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)

If qualifying AND all practices are rained out or cancelled
the teams making the race would be:
#46 Past Champion - 1988 Elliott [40th in Owners pts, 7 attempts]
#71, 36th in Owners pts, 7 attempts
#37, 37th, 7
#36, 38th, 7
#38, 39th, 7
#66, 41st, 7
#87, 43rd, 7
#60, 44th, 7
missing the race would be:
#15, 47th, 1
#97, 49th, 1
#35, 0, 0

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 that started 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. 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 2011 Past Champions Provisional Page for more.