My procedure for this is probably going to differ greatly from others, but here's what works for me. I started doing this after listening to a talk from vinney and jamil.
Also take into account all of my fermentations take place in stainless temp controlled conical fermenters.
Once primary is finished, meaning my final gravity has been achieved (usually 1.008) and DMS, diacytal, and all sulfides have either been consumed by the suspended yeast or I have re-pitched a low flocculating high attenuating yeast, I harvest my yeast for slants. I then pressurize the conical with 3 PSI C02 to ensure all O2 has been expelled from the fermenter. From there I can dry hop, add oak, add Brett, or simply let the beer mature without touching the finished product. I drop the temp from my ale fermentation temp of 59* F to 34* F. I do not put a time limit on this, but rather draw samples from the ball valve on the fermenter until the beer has decided it is at optimal packaging profile meaning taste, mouthfeel, and aroma.
For carboys I would use the racking cane and the carboy hood. Start the siphon by placing a sterile tube on the nipple of the carboy hood that does not have the racking cane running through it. I like to condition in kegs if l do not for some reason have a conical available. Connect your C02 to the "in" popit of your keg and purge the container with C02. Then connect the C02 to the tube on the carboy hood and use the pressure of the gas to start the siphon. This way no O2 is introduced during racking, and no O2 can penetrate the conditioning vessel. Of course you should be siphoning with a tube that either rests on the bottom of the keg or transfer through the dip tube in the keg to keep the procedure as closed as possible and to not splash the beer around at all.