This seems like a rather superfluous topic but I'm interested to know how people do the physical action of capturing pieces, particularly under high time pressure such as in blitz. Do you pick up the opponent's piece before moving your piece to the desired square? Or do you move you do both in one smooth motion?
This is the proper way to capture!
It depends of how "crowded" that part of the board is. If there are no pieces on adjacent squares of the destination I push the captured piece with my piece and take the captured piece off the board. This is one smooth hand movement. Then I usually use the captured piece to push the clock.
However, if there are many pieces next to the captured one I cannot risk dropping them off because adjusting would cost me precious time. I take the captured piece with my right hand, get it to my left hand and move my piece. By handing the opponent's piece from my right to left hand I save some time (compared to putting the captured piece out of the board first and then moving my piece).
In extreme time trouble I sometimes just throw the captured piece out, provided there are no kibitzes around my table
If I'm using one of my old or plastic sets I usually capture by pushing the captured piece off the square with the capturing piece as I pick it up. It's hard to describe but it's an easy and fluid movement. If I'm using my good set I always pick up the captured piece and then place the capturing piece on the square. No knicks, knocks, or bumps allowed for that set.
Just push your piece against the enemy piece with full force, hopefully even striking the rest of them out of the board, just like in bowling.
That sounds really action-packed.
Isn't using two hands illegal though?
Hover your hand over the piece you'd most likely want to move, then wait for your turn, thinking at the same time. Then your clock rises, finish up your thoughts, decide on the best move, then slide the piece to the new square or pick up the piece and put it down on the new square while the hand travels a perfect arc.
If it's a capture, push the piece into the captured piece and replace it with your piece (as dzikus suggested) and press the clock with the captured piece, or if the board is crowded, take the to-be-captured piece, put it between your teeth, place your piece on the square, hit the clock, then take captured piece out of mouth (or spit piece out of mouth).