Are you supposed to remove the piece before you take it or push it off the square as you take it?






Rarely I'll pick up the piece being captured first, but sometimes I just spontaneously do, probably most often it's because a knight is capturing, and there are a lot of pieces in between.
Otherwise I move my piece with thumb and pointer, and when it gets close to the piece being captured, I pick it up with my middle and ring finger. So it's sort of a simultaneous swap.
Rarely do I see people "push" one piece with another. It may be considered rude if the set is very nice, because it might dent or otherwise damage the piece (old wooden pieces will start to splinter at their base).


Yes, in this case you have to take the piece
Yes, in this case you have to take the piece
happened to me in a tournament once. I was playing black against an 8 year old kid. I had been nice to him the whole game, like allowing him to take back two moves because 1) he was about to get his queen captured and 2) he illegally tried castling through check. we were finally in an endgame where I was up a knight, and he moves his pawn but puts his pawn between two squares. I go to put the pawn on the center of the square where he meant to move it, but then he tells me that because I touched his pawn I have to take it. he calls up the TD who says the same thing and that if you want to adjust either your own your opponent's pieces it is required to say "adjust" before doing so. I take the pawn with my knight, he captures my knight with his other pawn, and I take that second pawn with my rook, effectively putting me up two pawns. I later take another of his pawns, making me three pawns up and win the game easily.
wow
once, my opponent accused me of touching his queen, which if i took with my piece would make him win in one or two moves. when someone suggested we call the TD, he said it was ok and e can continue. then he went out from the playing hall and came back with his dad, crying. the TD asked witnesses, but they didn't see if i touched it, although they heard him say it's ok. we continued the game normally and i won (i was up a lot). later the TD said the boy had already accused his opponents before of stuff like that.

A master once told me he gets annoyed when people take their piece, and push his out of the way when taking. He prefers removing the piece first, then gently placing your piece there afterwards. Is this proper etiquette? How do you take pieces??
I remember watching a video where they explained this. I hope I remember correctly. (The video is in the YouTube channel Circulo Jose Raul Capablanca but I can't remember the title). My recollection is that they're both correct as long as you use the same hand to move your piece, take your opponent's and hit the clock. The reason "el Capa" (Pablo Argüelles) gives for preferring to move his piece first is that sometimes as you're on your way to capturing you may notice a threat at the last minute. If you've already touched your opponent's piece you must take it But, if you're moving yours, you may decide at the last minute not to take and place your piece somewhere else. If you want to avoid "pushing" your opponent's piece you can use Fischer's hook, a technique demonstrated in the same video whereby once your piece has reached the piece you'll be taking, you take with two of your fingers while placing your piece on the square with the remaining fingers.
https://drive.google.com/open?id=0ByTuOnw5efVjakJxQVRQelFNWnRzZlduNWlGa0Uzbm5rdXFZ
https://drive.google.com/file/d/0ByTuOnw5efVja09mV0w5NWhLM1A2YXozMkVmdHo5M3ZDN3dv/view?usp=sharing
These are the two techniques I use. 95% I use method #1, but in special circumstances #2 is appropriate. Notice how in #1, I grab the opponent's pawn while moving my pawn simultaneously.

I pick up the eliminated piece with my left hand, and place the piece I am moving with my right hand.

(I haven’t played in a tournament. Maybe it’s time to practice picking up the piece with one side of my hand and dropping the piece with the other side.)

Yes, in this case you have to take the piece
happened to me in a tournament once. I was playing black against an 8 year old kid. I had been nice to him the whole game, like allowing him to take back two moves because 1) he was about to get his queen captured and 2) he illegally tried castling through check. we were finally in an endgame where I was up a knight, and he moves his pawn but puts his pawn between two squares. I go to put the pawn on the center of the square where he meant to move it, but then he tells me that because I touched his pawn I have to take it. he calls up the TD who says the same thing and that if you want to adjust either your own your opponent's pieces it is required to say "adjust" before doing so. I take the pawn with my knight, he captures my knight with his other pawn, and I take that second pawn with my rook, effectively putting me up two pawns. I later take another of his pawns, making me three pawns up and win the game easily.
Ups! Yes, we have always to say j'adoube (or, as you said, adjust) before touching a piece which we wan't to move or to take. Btw, I would not allow anybody to take back, even a 1 year boy. If you want to help him you take your time to analyse the game with him, if he wish. If you are playing for fun you can play handicap games, given your opponent a rook or a queen. Or you can offer him to turn the board when you have a winning position. And turn again if he is losing again, and so on. But no take-backs!
A master once told me he gets annoyed when people take their piece, and push his out of the way when taking. He prefers removing the piece first, then gently placing your piece there afterwards. Is this proper etiquette? How do you take pieces??