For me, the quickest way to legendary a skill is to farm Block using a shield with the giants at Guldun Rock. Obviously I kill one and leave the other alive, and when I get low enough on health I just run into the nearby cave to heal and/or wait. I do this to level so I can train 5 skill levels in something else, sprinting away when I do gain a level. It actually goes pretty quick (maybe an hour to cycle though another round of Block with the Lover/Warrior stone combo on Aetherial Crown and you raise several levels during that time) but it helps to be high level with good armor and heath enchantments. I think the most I've ever raised Block was 14 times with my level 101 Breton).

Another good way is to farm Conjuration by soul-trapping a corpse. That goes quickest if you have Conjuration/Magicka enchantments of course. Any other ideas? You guys do anything else?

restoration loop for high enchantments.
Make high smithing enchantments.
Make an iron dagger or hide bracers.
improve it. instant 100 smithing and over 1,000,000 value.
sell it for instant 100 speech.
legendary both skills.
repeat.

or swap smithing for alchemy.

Spam muffle for 100 illusion

Craft dwarven bows for smithing

For block, light armor, heavy armor, and restoration- I just let giants wail on me.

For alteration- I spam detect life in a major city.

Illusion- I spam muffle.

Smithing- make jewelry. This can also benefit alteration with transmute and speech from selling.

Conjuration- conjure bound weapons numerous times in combat. I don't really get into reanimating or daedra.

Restoration- I think there was a 'circle of protection' spell that gave some pretty good XP.

One-hand, Two-hand- battle trolls with weak weapons and no skill points in the tree. The trolls heal over time, so you can keep hitting them if you don't finish them off.

I thought one of the patches fixed the soul trap on a corpse loop.

Not on the legenary edition on console, i dont know if a patch on PC is there, maybe the unofficial skyrim patch fixes it.

But yeah, i know for legendary edition of skyrim, soul trap on a corpse is uneffected.

Cool. I use Skyrim Redone, which does fix alot of those "exploits", and couldn't remember how vanilla was.