Checking the gravity and sampling

if you brew in an open bucket you can use a clean turkey baster. don't blow air into the beer.
same with a carboy, but you need a long baster. or a 3/8" tube with your thumb over one end. similar to a wine thief.

don't sweat the risk of introducing oxygen. if you are careful there is not much risk. fermented beer has CO2 in liquid and there will be a blanket of gas over the surface of the beer.

that said, you should avoid leaving your beer in a bucket for an extended period as the surface area is large compared to the neck of a carboy. and don't slosh it around once fermentation has been completed.
Cheers.

 

Basically, you do it quickly and gently. You'll still get more O2 into solution than if you hadn't removed the airlock/cap/lid, but that's life. Some may say that there's a CO2 Blanket that will prevent oxygen from reaching the beer. It's true that there is CO2 in the headspace, but it's not some sort of impenetrable barrier.

 

CO2 blanket and additionally if the yeast is still actively metabolizing wort sugars, any minuscule amount of O2 introduced will be taken up by the yeast.

 

In short: You don't.

As said above, just try to work quickly, quietly, and with sanitation.

 

I...for one...do not say "...you should take a few graivity readings to make sure it has bottomed out so you are ready to bottle."

I just wait three fulll weeks before bottling instead of taking "...a few graivity readings to make sure it has bottomed out so you are ready to bottle."

 

Same here. But if you want to be sure, that's the way.