Examples

Black can trade knights with 1...Nxe5. After White recaptures with 2.Rxe5, the rook is lured to e5, where Black can attack it with the pawn fork, also attacking the bishop on g5 at the same time. Note that f6 immediately does not work because of Nxd7 (or Nxg6).

Here is a typical example from the opening:

White can win by trading with 1.Bxa6 Nxa6, luring the knight into the queen fork 2.Qa4+ Qd7 3.Qxa6.

The other order doesn't work: 1.Qa4+? Qd7 (now the queen is attacked) 2.Qxd7+ Kxd7.

Sometimes a trade can be combined with deflection:

The queen on f2 is protecting the rook on h4, and the square f3. It is overloaded, and Black can win with 1...Rxh4, combining trade and deflection. After the queen recaptures with 2.Qxh4, it is deflected away from protecting f3, and also lured to h4. Black can now win the queen with the royal fork 2...Nf3+.

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 fork.
Instead of a trade, a decoy uses a piece sacrifice to lure a piece to a square.