The most basic stomp switches are double-pole double-throw (DPDT) switches. There are many ways to implement signal switching, but this is the simplest:
When the switch is in the 'Effect Active' position, the signal flows out of the guitar, into the input jack, through the switch, through the effect circuit (the one you posted), back through the switch, and out of the pedal
through the output jack.
When the switch is in the 'Effect Bypassed' position, the signal is routed directly from input to output. This is 'true bypass' switching. You might hear noise when you activate the switch because the switching action produces a discontinuity in output signal.
simulate this circuit – Schematic created using CircuitLab
The two pins on the switch that don't move are the 'poles'. The pins they switch between are the 'throws.' Stomp switches are also available as 3PDT. You can use the third set of contacts to turn an LED on and off, among other things.
More complex schemes with other kinds of switches are commonly used, but they tend to be far more complex than your effect circuit. This site has an analysis of the buffered bypass switching used in Tube Screamers: https://www.electrosmash.com/tube-screamer-analysis . It uses a normally-open momentary switch that toggles a flip flop. The two states of the flip flop control JFETs that act as switches.
With buffered bypass your guitar signal always flows through a signal buffer in the effect circuit. Whether or not it makes sense to do that depends on the overall complexity of the circuit and what switches you have available and can fit into your enclosure. In the case of the Tube Screamer, it is mandatory because of the way the switching circuit works, and the switching circuit is designed that way because of the switch that is used. You could also use buffered bypass with a mechanical switch. There are lots of options.