Learning to salute the right way. Either you are doing some research before basic or you got into trouble and were to lazy to look up the regulation to see how to salute the right way. Either way, you are in luck. Here we go.
First, you need to know that this guidance and direction of saluting appropriately according to the Army comes from TC 3-21.5. It varies slightly depending on headgear or eyewear. The positioning is generally the same but the point of reference for the finger tips adjusts according to the headgear or eyewear worn.
Here is the guidance straight from TC 3-21.5 as of 20 January 2012.
4-4. HAND SALUTE
The Hand Salute is a one-count movement. The command is Present, ARMS. The Hand
Salute may be executed while marching. When marching, only the Soldier in charge of the formation salutes and acknowledges salutes. When double-timing, an individual Soldier must come to Quick Time before saluting.
a. When wearing headgear with a visor (with or without glasses), on the command of
execution ARMS, raise the right hand sharply, fingers and thumb extended and joined, palm facing down, and place the tip of the right forefinger on the rim of the visor slightly to the right of the right eye. The outer edge of the hand is barely canted downward so that neither the back of the hand nor the palm is clearly visible from the front. The hand and wrist are straight, the elbow inclined slightly forward, and the upper arm horizontal (1, Figure 4-5).
b. When wearing headgear without a visor (or uncovered) and not wearing glasses,
execute the Hand Salute in the same manner as previously described, except touch the tip of the right forefinger to the forehead near and slightly to the right of the right eyebrow (2, Figure 4-5).
c. When wearing headgear without a visor (or uncovered) and wearing glasses, execute
the Hand Salute in the same manner as previously described, except touch the tip of the right forefinger to that point on the glasses where the temple piece of the frame meets the right edge of the right brow (3, Figure 4-5).
d. Order Arms from the Hand Salute is a one-count movement. The command is Order,
ARMS. On the command of execution ARMS, return the hand sharply to the side, resuming the Position of Attention.
e. When reporting or rendering courtesy to an individual, turn the head and eyes toward the person addressed and simultaneously salute. In this situation, the actions are executed without command. The Salute is initiated by the subordinate at the appropriate time (six paces) and terminated upon acknowledgment. (See Appendix A for more information on saluting.)
Department of the Army. (2012). Drill and ceremonies. Training Circular, 3-21.5, 4–6-4–7. https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/tc3_21x5.pdf