A quick "tutorial" to give you a way to do it.
First, join all the robot parts. As you used some mirrors but all parts are not symmetrical you may need to correct some geometry (but I let it as is here).
To join all the part, select them all (border select B is good here), then choose a central part to be the main object and Shift select it so that it become the active (but keeping the others selected).
Now hit Ctrl+J to join them all in one mesh.
As I said previously, all is not symmetrical here so you need to rework a bit in order to have a correct mirror symmetry (not visible in object mode but will have some consequences on the rig).
Now place yourself in front view, in face of your robot.
Add an armature (A then armature and single bone). Check "X ray" in the display section so that it will be visible even behind the robot.
Enter edit mode Tab on the armature, move it vertically along Z G+Z, then move the bone's head along Z too in order to make the main central bone for the body.
Extrude it by selecting the bone head then E to extrude and move to place the shoulder. Extrude again for the arms parts.
Then go to the size view Numpad3 and adjust the positions of the bones extremities.
(you can go ahead with the finger with the same technics but I will not do it here)
Rename the bones. This is much easy after that.
In particular for the symmetrical parts, you can suffix (for instance) them with the side they correspond to.
That allows Blender to understand what is what so that you can generate the opposite side automatically using the 'symmetrize' command.
As your robot is more "articulated parts" than "organic linked parts", I think it is better here to parent the robot to the armature this way :
Select the robot and Shift select the armature (in this order) and Ctrl+P to parent. Then choose "with empty groups".
That will create vertex groups in the robot. These groups have the names of the bones.
Now assign each vertices parts of the robot to its corresponding group name.
To do that : select the vertices, click on the group then click "assign".
Here is the result below. For convenience you can activate the "auto IK" (automatic inverse kinematics).
As you can see, this is not symmetrical : this is due to the mesh which needs a bit clean up to be symmetrical itself.
You can also "skip" the shoulder here, as it may be unneeded (this is your choice). To do that, don't create it and extrude the upper arm directly but make it not connected :