Step one: reinforce the framing so it won't fall down on me. I installed some ceiling joists / collar ties to the rafters to prevent the roof from spreading. There have historically been a couple of 2x4's nailed across the top plates, but no support for the rafters themselves. A couple have crept out a few inches, and I might lift the center of the roof and pull them back in with a winch later on.
Then I installed a piece of OSB sheathing at one end of the building, screwing it pretty densely to the framing, to provide shear resistance. That let me cut a pretty big access hole in the back wall, relieving some weight and making it easier to move materials around.
To do the actual lifting of the building, I sistered some short studs to four sets of opposing studs on the side walls. Cutting slots in the siding with a plunge saw let me to run 2x6x16' lumber across the width of the building, with 2' sticking out each side. The 2x6's are then screwed to the side of the primary studs, to keep them from flopping sideways, and prevent the lower part of the walls from spreading. These beams bear upwards on the bottom of the short studs, which bear up on the top plate and are also lifting the regular studs through the fasteners.
I jacked up one side of the building at a time, using a motley of jacks I have around, from a 20-ton bottle jack that could lift the whole building to a little screw-up scissor jack that's meant for changing a car tire in an emergency. Those little jacks are weak, and a little tippy, but they start really short and have a wide range, so they're handy, and easy to get at a junk yard. I put a jack under each of the four beams and lifted a bit at a time until things were where I wanted them. I then went outside and installed a stack of two concrete cinder blocks, sitting on 2x12 wood pads, to support the building while other work was done. They're cheap and have good compression strength. Repeat for the other side, and it's hanging in the air.
The 2x6 lifting beams definitely deflected some, but by keeping the points of support near the walls (either jacking from inside or on the cinder blocks outside) the actual stress on the lumber was not a big deal. I was able to walk on them and work on the building with very little fear.