We found the "all done" sign helpful in figuring out when our children weren't hungry....often the throwing is boredom and disinterest in food. (also, it's really cool to throw.) One yr olds are all about learning cause and effect. They want to know what happens when they....hit, throw stuff, screech, etc.
1) offer acceptable alternatives. "You can throw this ball or this pair of socks" (better to say what they can do than what they can't.) The idea of "do not" is pretty abstract for a one yr old.
2) know that babies (and he is still a baby) have developmental needs that they will do their best to meet (learning to throw, climb, etc.) (see suggestion one :) )
3) be consistent with your responses. If you laugh once b/c he hits you in a playful way, and then the next time you get sad, and the next time you get mad, he will keep hitting to see what will happen next. Simply and calmly say something like "hands are for gentle touch" and show him how to touch you gently. I started quite early with my kids telling them that if they hit, bit while nursing, etc I would put them down for a minute. I was never angry or harsh, just "Mama doesn't like to be hit." The behaviours stopped easily once the baby knew it wasn't okay.
4) understand that he is not at 15 months capable of empathy, and is most likely mirroring your responses. True empathy comes into play at about 5. I mention this b/c I found it frustrating with our middle daughter when she would act so empathetic on moment and then do something unkind the next. I found my expectations of her were often not age appropriate b/c I believed her capacity for understanding other's emotions to be so much greater than it actually was.
5) understand that at 15 months, a child has very little to no impulse control. Just b/c mama said no last time doesn't mean that he retains that or is able to apply it to the current situation. (for example, the draw to throw stuff may be so much stronger than his ability to look at the thing he wants with all his little body to throw, and to restrain himself from throwing it b/c mama said no last time. (In other words, expect to go through the same issues again, and again and again :)
6. Best to prevent unwanted behaviours by close observation and really knowing your son (which I'm sure you do.) For example, what happens before he hits? Is he hungry, tired, bored? Etc etc.
Hope some of this helps, sorry it's a mini book. :)