UPDATE#1 2018_12_05 (simpler circuit)
Hi nyame
The 555 timer is a good chip but it is not really suitable for some applications. As a result of this, the other members have given simpler and better circuits. But if you must use a 555, attached is schematic for a 555 toggle circuit for you.
When the circuit first powers on, the output will be set to 0V, and the LED will be off. The first time you press and release the switch, the 555 will toggle and the LED will illuminate. The next press and release and the 555 will toggle again and the LED will go out...and so on.
The circuit has built-in switch denouncing so you will not get multiple toggles each time you press and release the switch.
If you press and hold the switch the 555 will oscillate. C3 defines the switch denounce inhibit. C3 also defines the frequency of oscillation when the switch is held on. You can experiment with different values of C3 to tune the circuit to your liking.
Notice that the 555 Q output is not involved in the toggle function, so the Q output can be used as you wish.
For a low current, low voltage role like this, the switch should have gold contacts, or other contact material suitable for low level signal switching.