I've made this before using smoked turkey, but usually use a smoked thigh or a couple of smoked wings. The outcome of the dish seems to depend on how salty the smoked turkey is. I've found some brands to be outrageously salty.
Anyway, I buy my greens - approx. 1/2 to 3/4# each of kale, collards, mustard, turnip - whatever's available & looks nice & fresh. I then wash well & remove & discard all heavy stems. The remaining leaves are roughly chopped. I saute an onion in some extra-virgin olive oil until soft but not browned. Sometimes I'll add a chopped clove or 2 of garlic as well. Then in go the greens & I stir them around till everything is slightly coated with the oil. I then add a cup or 2 of chicken broth (Swansons, usually), & my piece of smoked turkey, bring to a simmer, cover, & cook just until the greens are done to the tenderness I want & the smoked meat is heated thru. I then remove the poultry piece, remove the meat, shred or chop it, & return it to the pot & serve.
I don't like to stew greens (even collards) for the long amount of time most recipes call for. If they're fresh & not overgrown, they won't be tough or bitter with a shorter (& more nutritious) cooking time.