I've looked through the Shimano Technical documents and it states the chain should be on the largest chainring and smallest cog in order to determine the length. Next, it mentions that the pulleys should be perpendicular to the ground. What i'm not sure about is if the pulleys and the center of the freewheel all have to line up to perpendicular or is it only the two pulleys that need to line up and be perpendicular?
I have a double setup..105 front, ultegra rear, 9 speed chain...if that makes any difference.

run the chain around the large chainring, and the largest cog (dont run it through the rear derailleur yet)
then add 2 links (some people only add one link, but ONE time I came out with a chain that was too short, so I add two links)
Then seperate the chain there.
Run it through the derailleurs, and you should be good to go.

Exactly right.

The Park Tool site has a good section on this. They recommend the same method as the above two posts, and also have a way to calculate the length using the number of teeth on the largest ring and cog, and the distance from the crank axis to the rear axle.

I'm working on installing a new drivetrain, including the chain of course, so just for fun I'll see how the calculation compares to the fit + 2 method.

This is the SRAM method. OP refers to Shimano method, which is big+small+vertical. Shimano refers to the pulleys being on top of each other, regardless of where the freewheel happens to be - most probably behind. Both methods will lead to different chain lenghts, depending on largest cog in back (Shimano method does not take the size of largest cog into account). I prefer the SRAM method (big+big+2) since it addresses the one limitation of chain length: being able to accomodate the most extreme situation, i.e. big+big.

https://www.bikeforums.net/search.php?do=process

Exactly and this is a critical fit issue. We all know you shouldn't ride in big-big but one time at least, due to brain-fade or needing a lower gear in a rush, you will wind up in that combination. The chain must allow it or the resulting damage will be quite impressive.

The Shimano method works but assumes you are within their published tooth differences and total teeth ranges for the rear derailleur, chainrings and cassette. If you take any liberties with these recommendations, the chain maybe too short.

I used Sheldon Brown's article in combination with the Park site. One thing I found - chain links either have the metal faces on the outside or the inside. (I'm not sure if I've got my terminology straight, but look at a chain and, hopefully, you'll see what I'm talking about.) An "outer link" has to connect to an "inner link". Therefore, sometimes you might have to add or subtract a link to your "perfect length" to make this come out right. All I know is that I installed two chains this summer using these sites, and both bikes work fine. It wasn't that tough.

When faced with this problem, use the the longer configuration.

It has nothing to do with the freewheel center. It means that a line through the two pulley wheels is at a right angle to the ground. The dérailleur pivot spring will locate the RD however it sees fit, and that won't change the measurement.

IMO the Shimano method is at least as good as the "big-big" method, but isn't as easy to use perform.

Conversely, it may be too long. No method can accommodate a wrongly sized dérailleur. The Shimano method at least centers the arm range to minimize the effects at either end.

thanks to all that replied. I ended up going the shimano perpendicular method. All is well...so far..

..now about this b-setting thing???....

Too long a chain is only a nuisance and keeps you from effectively using the small-small combinations. If you do inadvertently use small-small no harm is done, the chain just hangs loose.

Too short can lead to catastrophic damage so if there has to be a choice, other than perfect, go with too long.

BTW, big-big+2 will give you the proper chain length if you are within the recommended tooth count for your rear derailleur and will allow you to use small-small without the chain going completely slack.