First, understand that there can't be more than 2 teams from any conference in the BCS bowls. That is key.
Second, BYU gets an AUTOMATIC berth only if they are ranked in the top 16 AND they are ranked higher than any champion of any BCS conference.
With that in mind, here is what has to happen for BYU to get in (slim chance):
1. BYU COULD get in if ranked in the top 16 and ranked ahead of the conference champion of any BCS conference. The only conference for which this has any possibility is the Pac 10.
UCLA would have to beat USC, AND UA would have to beat ASU. If both of those things happen, and if BYU is in the top 16, they are in (assuming a Hawaii loss- Hawaii would get the pick automatically for being ranked higher than BYU). That is a lot to hope for, though possible.
OSU does NOT have to beat Oregon. If Oregon beats OSU, UCLA beats USC and UA beats ASU, then there is a 4-way tie in the Pac 10 with Oregon, UCLA, USC and ASU. UCLA wins the tiebreaker and goes to the Rose Bowl (and BYU would be ranked higher than UCLA, thus getting the automatic berth).
If OSU beats Oregon (and the other games described above go as hoped), there is a 4-way tie in the Pac 10 among OSU, ASU, USC and UCLA. OSU wins the tiebreaker (as unbelievable as that may sound) and BYU is ranked higher than them, thus getting the automatic berth.
The tiebreakers are explained here for the Pac 10:
http://latimesblogs.latimes.com/allthings trojan/2007/11/ducks-fowl-thin.html
BUT, the trouble is that 3 teams ahead of BYU have to fall below 16 (to allow BYU to rise to at least 16).
Most likely candidates: ASU (which has to happen anyways), Oregon (could happen), Tennessee (likely to happen), Hawaii (has to happen anyways), Boston College (they would need to get pummeled).
In other words, 2 teams ahead of BYU have to lose for BYU to get in anyways. That leaves 1 team of any of Oregon, Tennessee, or BC that must also lose.
SUMMARY:
TEAMS THAT MUST LOSE-
Arizona State
Hawaii
USC
One of: Tennessee, Oregon, BC (and BC would have to lose big)
And who would we play?
ACC- champ goes to Orange (winner of VT/BC) v. at-large
Rose- Ohio St. v. (Oregon St. or UCLA)
Fiesta- 2 slots for at-large teams open
SEC- LSU or Georgia in Sugar v. at-large
BYU could play in any bowl other than the Rose Bowl.
Fiesta gets the first pick.
Sugar picks 2nd.
Orange picks 3rd (BYU could beat VT or BC, I think).
Then Fiesta picks again.
2. BYU cannot possibly get an at-large berth for the following reasons:
Understand that if a team is in the top 14, they must be selected as an at-large pick (after all automatic picks are finished) before any team from 15-18 (unless their conference already has 2 picks).
Based on the BCS polls right now, the conference breakdown for the top 16 is as follows:
SEC: 4 teams (Georgia, LSU, Florida, Tennessee)
ACC: 3 teams (Virginia Tech, BC, Clemson)
Big 12: 3 teams (Missouri, Kansas, Oklahoma)
Big 10: OSU, Illinois
Pac 10: USC, ASU
Big East: West Virginia
WAC: Hawaii
The SEC is assured of filling 2 slots.
The Big 12 is a lock for 2. No matter what happens with Missouri and Oklahoma, they will have both slots filled.
The ACC could have a team drop out of the top 14, but regardless, they should have 2 locked for BCS games (since Clemson is done playing and presumably won't be jumped by BYU).
The Big East will only have 1 team- West Virginia.
In the Pac 10, Arizona COULD beat ASU, and OSU COULD beat Oregon (and USC could still win). IF those two things happen, Oregon would definitely fall past BYU (they are currently 17, BYU is 19) and ASU could also fall below BYU (they are currently 13, so a big loss to UA would drop them quite a bit). If that happens, then the Pac 10 only has 1 team in the top 16 to select.
In the Big 10, OSU is a lock (automatic). If the Pac 10 shakes out like described above, Illinois would get the remaining spot. Otherwise, the Pac 10 gets 2 spots and Illinois is left out.
So, 10 spots to fill.
SEC: 2
ACC: 2
Big East: 1
Pac 10: 1/2
Big 10: 2/1
Big 12: 2
Basically, our hopes hinge on the Pac 10 champion being ranked below BYU and BYU being in the top 16.
Clear enough?
Oh, and of course BYU must beat SDSU- you can't take anything for granted.