Keyboard:

A+D to move

W to jump

[space] to dash

S to enter downward-facing pipe

E to open map

left click to shoot

right click to open chests and pickup items

Controller(I have only tested with an Xbox controller):

Left joystick to move

Left trigger to jump

Right trigger to dash

Left joystick down to enter downward-facing pipe

left bumper button to open map

Right joystick to shoot

A button to open chest and pickup item