How Do I Programatically Attach Objects To Each Other?

Set transform.parent = otherObject.transform to attach this object to the other object for example.

When attaching objects, I also found it useful to disable collisions on the object being attached. For example:

 // Disable collisions with the object being attached
 if(Object1.collider2D)
 {
     Object1.collider2D.enabled = false;
 }
 
 // Don't allow physics to affect the object
 if(Object1.rigidbody2D)
 {
     Object1.rigidbody2D.isKinematic = true;
 }
 
 // Attach object 1 to object 2
 Object1.transform.parent = Object2.transform;
 
 // Center object 1 on object 2 (no offset)
 Object1.transform.localPosition = Vector3.zero;

Just make sure that you watch the relative positions & rotations.

I have:

 GameObject objA=...;
 GameObject objB=...;
 // attach a to b
 objA.transform.parent=objB.transform;
 // make sure its exactly on it
 objA.transform.localPosition=Vector3.zero;
 objA.transform.localRotation=Quaternion.identity;

And its fine.