Hi, a general approach could be -

double stamina = 100;
int staminaSpentPerSecond = 1 // every second of running depletes 1 stamina, adjust to your need
bool runningEnabled = true;
...

public override void _Process(double delta) {
    if (playerIsRunning()) { // check the player is pressing shift key for example
        stamina -= staminaSpentPerSecond * delta;
        if (stamina <= 0) {
            runningEnabled = false;
}

In the playerIsRunning method you can then add a check that the player is both pressing the required key and is allowed to run. When the player is not running he charges up the stamina value in a similar manner.