So far, we have accomplished stepping up one step, but this is only half of the process necessary for reaching something on a high shelf. The second step, of course, is reaching up with the arm to grasp the desired object. The beginning of the process is pretty much the same -- a nerve impulse originates in the brain (possibly in the motor cortex for this more complex and less-often performed task), and then travels along the spinal cord and periphery nerves to the proper muscles (pbs.org). Again, the neuromuscular junction is the site of chemical/electrical messaging between he nerve and the muscle fiber, and the same process activates the muscle tissue.

It is worthwhile to examine exactly what process takes place in the muscle tissue once activated that actually enables movement. muscles work by contracting; at the cellular level, the muscle fibers actually cling together and shorten when activated, and are able to relax but not push in the opposite direction (Freudenrich 2009). This is why muscles often operate in oppositional pairs, so that one muscle can perform the opposite action of its partner. In order to accomplish this feat of contraction, the spreading chemical messenger causes the calcium stores located in the muscle tissue to open (Freudenrich 2009). The calcium ions flow into the cytoplasm of the muscle cells where it binds to troponin-tropomyosin molecules located in grooves on the actin filaments. These molecules normally prevent myosin from bonding with the actin, keeping the muscle from contracting. The calcium ions change...

The connection of the fibers draws the muscle tissue closer together, contracting the tissue which in turn pulls on the bones of the skeleton and creates movement.
Again, this process is largely the same for all skeletal muscles, but there are very specific muscles involved in raising the arm to reach something on a high shelf. The shoulder is another ball-and-socket joint officially known as the glenohumeral joint (Cluett 2009). The humerus -- the bone of the upper harm -- attaches to the glenoid, which is a part of the scapula (the bone that forms the shoulder blade), and swings when moved by the four muscles that make up the rotator cuff (Cluett 2009). These muscles would raise the humerus, rotating it upwards in the glenohumeral joint, as the triceps would help to extend the forearm (straightening the elbow) and keeping the arm held upright (Cluett 2009). Depending on the object being grasped, several of the many bones and muscles in the wrist and hand would become involved at this point.