Examples

Black just captured the pawn on d4 with Nxd4, but this was a typical opening mistake.
White can now win by trading knights with Nxd4.
After Black recaptures with Qxd4, the queen is lured to d4, where it can be attacked with the discovered attack Bxh7+!
The bishop sacrifices itself with check, and discovers the attack of White's queen on d1 on Black's queen.

The trade can also happen on the piece that is attacked directly, as in the following example:

Black just played Nc3, attacking White's rook and bishop, but this was actually a mistake.
White is forced to trade bishop for knight with Bxc3, but it turns out this is a winning move.
After Black recaptures with Rxc3, the rook is lured to c3, where it can be attacked with Nb5.
The knight also discovers an attack of White's rook on d1 on Black's queen.
After the queen moves away, White wins the exchange with Nxc3.

Related combinations

It is also possible to use a trade to lure a piece to a square where it can be attacked in a subsequent tactic other than a discovered attack.
Instead of a trade, a decoy uses a piece sacrifice to lure a piece to a square.