Yikes! The whole middle has fallen.

I'd say that this goes way beyond the scope of a DIY project. The "method" is going to be bringing in a structural engineer and an experienced mason. Your talking about supporting the structure and then rebuilding it from the foundation up. Depending on how much water as gotten into those cracks, you could end up having to replace a lot of material.

That wall is an accident waiting to happen! If it can be restored, it will need to be done by someone heavily experienced in this area. Frankly, this looks worse than anything I've ever seen salveged. Does the building have super historic signifigance? At some point, buildings are past repair.

Your insurance company could possibly prefer to demolish it rather than to repair it. So you'd better have good financial reserves if you want to tackle this. You'd be assuming a big liability if your insurance company doesn't want to be involved. A structural engineer, lots of steel and professional masons will need to be involved. And money. Lots of money.

And I thought the foundation/structure was bad in the house im looking at purchasing. WOW!

Shnnn, perhaps some more info?

Is this a place you drive past on your way to work?

A place you're interested in buying?

Your property, that you've purchased already?

(A joke? Surely not...)

We had to rebuild a non-structural brick wall on the north side of our front porch. The mortar had cracked and the bricks were mis-aligned as a result of years of foundation water damage. This wall was about 7' x 8'.

Each brick was taken out 1 by 1. All mortar was hand chiseled off the bricks. We had underground foundation work done and then each brick was relaid. Our masons figured out the original mortar recipe and color so matched it when rebuilding the wall.

I would not even want to guess at what the cost would be to do similar work on the wall in your picture!

You need a structural engineer and a good mason. Be prepared for the news that the cost of repair exceeds the value of the structure.

This is a property I'm thinking of buying, and I definitely wouldn't tackle the job myself. I'm just interested in knowing if there are multiple approaches to the project or if every structural masonry team would approach it the same way.

You don't just need a structural engineer, you probably need a soil engineer to figure out what foundation problems are soil-related, and to top it off, a feasibility study for the intended use.
You have no water tight roof that I can see, probably no safe floors either, which means there are two unstable side walls to support/shore while the rear load-bearing wall is disassembled to the footer, perhaps beyond, then rebuilt. Months for the mason's crew, only then can you safely tackle the roof and floors, add windows and you will have a weather tight structure, which by the look of things needs all systems replaced from the street in.
Such a great project for the fortunate restoration contractor! If you can pay him.
If this were the rear of a 150 foot deep structure, it would probably make the best sense financially to pull down about 20 or 24 feet of it and put in a good foundation without having to stabilize the side walls. The new could be wood-framed or masonry, but time would be saved either way.
Casey