Before going any further, it's best practice to get your buttons and motors connected and make sure they work as expected.
Connect the quick-connect wire pairs to the button terminals, and plug the male/male jumper wires into the JST connector at the other end.
Extend the Servo Arm
In the package with the servo are several plastic horns that can screw onto the servo. Select the one with two arms in a straight line.
Extend the reach of the servo arm by taping a bamboo skewer to it.
Plug each servo motor into the four servo ports on Crickit.
Optional 90° bend
For the arms that will connect to the legs, it may help to add a 90 degree bend, thereby extending the reach outward and forward at the same time.
Use hot glue to brace bends in wood skewers, then use tape and hot glue to affix the wooden armature to the servo motor hub.
Now you should be able to plug in your Crickit and check that pressing each button results in movement from its corresponding servo motor.