I'll assume a asphalt shingle roof. Starting at the top (ridge) shove your tear-off shovel under the caps and pry up. do this on both sides. Once you have a section of the caps removed, push shovel under the shingles (from the top) and pry them up. Do this until you have reached the bottom. Repeat untill entire side is torn off, making sure all the old roofing nails are pulled. This is why your shovel has teeth.
Wood shakes are best attacked going sideways, using a turning fork.
https://www.bestmaterials.com/images/AJC-117-SGS-WOOD-large-A.jpg Tear-off shovel
https://mobileimages.lowes.com/product/converted/049206/049206645172.jpg Turning fork
Can verify is actual roofer, I spent 3 weeks working on a roofing crew, I figured there had to be a better way to tear off than how we were doing it. Like some kind of strategy to keep things cleaned up easier after the tear off is done, it seemed like half the job was clean up after the roof was done.
With practice and shingles that aren't too crumbly, you can get them off whole and stack in a pile for the labor person to throw in whatever you're using to haul them away in.
That would probably work better, everything just got tossed off the roof onto tarps on that crew and it was a mess.
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