need to use chains not twine
double hitch the chains, one hitch above the pastern/ankle, the other below or just above the hoof; this spreads out the pressure of the pull
need to use a puller
work with the cow/don't be in a hurry; tighten the pull just a few clicks each time the cow strains; but don't click it up everytime; about every other time, when the cow strains, just drop the puller down to the ground, put it back up, then the next time take up the slack a few clicks
slow and easy helps alot
you can go really slow until you get the calf about halfway out then the navel cord becomes compressed on the pelvis but the calf is not out far enough to breath on his own, and you need the to get the calf out quickly until that point is past or when the hips are left in the cow; then the calf is out far enough to breathe and you can give the cow/calf a rest again.
I can't say that it is any harder or easier to pull a calf with the cow standing up or laying down; just a bit different.
If the cow is laying down, then you have to be sure that she is FLAT down; doesn't have a leg tucked underneath her as they most often do when they lay down to rest....and very important for both cow/calf is that you go straight down with the puller once you get the calf about half way out; that is a much more natural position for the calf rather than pulling it straight out in a parallel line which puts alot more stress on the calf's back, more chance of injuring the cow also.
I hope you can understand what I have tried to convey; in many, many, many pulls over many years of raising cattle, I have never broke a leg.....I am thankful to the amazing cattle vets that have taught me over the years how to correctly pull a calf....any more questions, pm me or post.