Hi Buddy:
There was some support, historically, for the method that you describe (I.e. Reshuffling the exposed turn card back into the deck right away), and there are indeed some merits to that approach, but it is not (at least currently) the "standard" approach. The approach that is generally used today is to deal what would have been the proper river card as the new turn card after the flop action is duly completed. This preserves 4/5ths of the original board. The exposed turn card would only then be reshuffled into the deck if it is necessary to deal a river card.
If I were to break down the procedure step by step (forgive me if you do not require this level of detail):
1. Announce to the table that the turn card was dealt prematurely and will not play. Remove the exposed turn card from the board (usually keep it face up) and set it aside (e.g. close to dealer to the right of where his chip tray would be).
2. Direct action on the flop betting round to continue. In your example, you would have the player complete his raise. Note that if everyone then folds, you won't have to do anything so it's unnecessary to go into too much detail with what is going to happen on later streets at this point.
3. With action complete, announce to the table that you will now be dealing the proper river card in place of the turn. Direct your dealer to burn a card (now there will already be 3 burn cards) and deal the new turn card (what would have been the river).
4. Direct action on the turn betting round to continue. Some TDs will keep the exposed card still out, but I prefer to put it on the top of the deck at this point. This allows the card to be protected and you won't mistakenly forget to shuffle it back into the deck if you need to. No need to reshuffle yet though, since if one player bets and everyone folds on the turn, the situation is resolved.
5. With action complete, announce to the table that you will now reshuffle the exposed card back into the deck, so that it has a chance of reappearing on the river. Direct your dealer to shuffle the cards (including the exposed one). Be careful not to expose the cards when squaring the deck (a common error since dealers will square up cards facing the players as they would at the beginning of a deal out of habit). Announce to the table that the dealer will cut the cards and then deal the river WITHOUT BURNING, and then direct your dealer to do this. Action on the final betting round continues.
Note that some venues and rule sets favor burning a fourth card before dealing the river, but this practice has not been widely adopted. Thus, I believe it is best that you tell the players what is going to happen just before you do it as I've noted above, to avoid any misunderstandings.
I hope this is helpful.
K