You salute with your right hand unless your right hand/arm is incapacitated for some reason in which case you can salute with the left.
From the Navy BMR (Basic Military Requirements)
The following are some of the major points you should remember when rendering a salute:
1. If possible, always use your right hand. Use your left hand only if your right hand is injured. Use your left hand to carry objects and to leave your right hand free to salute.
2. Accompany your salute with a cheerful,respectful greeting; for example, “Good morning, sir”;“Good afternoon, Commander [Jones]”; “Good evening, Chaplain [Smith]”.
3. Always salute from the position of attention. If you are walking, you need not stop; but hold yourself erect and square. If on the double, slow to a walk when saluting.
4. Look directly into the officer’s eyes as you salute.
5. If you are carrying something in both hands and cannot render the hand salute, look at the officer as though you were saluting and render a verbal greeting as previously described.
6. Remove a pipe, cigar, or cigarette from your mouth or hand before you salute.
7. Salute officers even if they are uncovered or their hands are occupied. Your salute will be acknowledged by a verbal greeting, such as “Good morning,” “Good afternoon,” or something similar.
8. Army and Air Force policy, unlike the Navy’s, is to salute when uncovered. Suppose you are in an office with several Army personnel, and all of you are uncovered. An officer enters and the soldiers rise and salute. You should do likewise; to do otherwise would make you seem ill-mannered or disrespectful.
9. If you are walking with or standing by a commissioned officer and the occasion for a salute arises, do not salute until the officer salutes. Assume that you are walking with a lieutenant. A commander approaches. Do not salute the commander until the lieutenant salutes; but as soon as the lieutenant starts to salute, you should quickly do the same.
10. When approaching an officer, start your salute far enough away from the officer to allow time for your salute to be seen and returned. This space can vary; but distance of about six paces is considered good for this purpose. Hold your salute until it is returned or until you are six paces past the officer.
11. Salute all officers who are close enough to be recognized as officers. It is unnecessary to identify an officer by name; however, ensure that he/she is wearing the uniform of an officer.