Examples

Black can trade knights with Nxe5.
After White recaptures with 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).

Sometimes a trade can remove the defender:

White can trade knight for bishop with Nxb3.
After Black recaptures with Rxb3, the rook is lured to b3.
White can now attack the rook on b3, and the king on g8 at the same time with the queen fork Qe6+.
This is possible, because e6 is no longer defended by the bishop.

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 Rxh4, combining trade and deflection.
After the queen recaptures with Qxh4, it is deflected away from protecting f3, and also lured to h4.
Black can now win the queen with the royal fork 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.