What i would do is define a velocity variable initializad on zero. On each phisics processing step (i assume player is kinematic body) ill move the player according the velocity. I would connect
button_down signal of the button to a function that sets velocity to the value expected in movement, and
button_up signal to a fucntion that sets velocity to 0.
Something like this:
var velocity = Vector2(0,0)
velocity = move_and_slide(velocity) #assuming top down game here
velocity =Vector2(100,0) # or whatever you want
velocity = Vector2(0,0)
This is only ilustrative. With more info perhaps i could help more.