Hi,
That type of connector has 4 connections, 2 either side. They are switched connections. If you insert a jack plug you will see that 2 of the connectors pass over the jack and the other 2 connect to nothing once the plug is inserted. you need to solder wires to the 2 connections on the side that passes over the jack plug. The connection at the back of the connector is the positive ( tip ) connection and the other one nearest the nut is the ground.
If you connect an amp directly across the speaker it should work, then remove the wires from the speaker and connect them to the jack socket.
However one very important thing is that you must block any DC voltage, some toys can have a 5v DC ( or more! )level on the audio, which will not do your amplifier any good, so insert a polarised capacitor ( 10uF ) in series with the tip signal of the jack, with the negative side of the capacitor going to the tip and the positive side going to the speaker wire.
Cheers
Paul