how much time do you want to spend and do you want to do it by hand?
I too had "haze" spots and my dad(jack of all trades, also did body work most of my life, he just can't now hurts his bones, you know how old ppl are....lol) said not to let the dealership do it, they would just make a mess of it.
if you nitro is more than several months old follow this process....it will make you hurt, take ALL day but the results are gorgeous.
1. wash and dry as usual
I love mequire's so
2. get a claybar and lub for the claybar, follow directions on product
3. follow up with the #9 swirl remover-follow directions
4. use #7 show car glaze
5. finish with mequire's gold class paste wax
6. wait 12 hours and apply another coat of wax. wax every other month this will keep the swirl marks partially filled in and they will not attract the sun and show as badly. of course you can totally remove them by using a hand buffer, but I am not into power tools and did not want to risk more harm than good. my dad said he will do it for me when it gets cooler down here.
good luck, I did this full process last weekend and am satisfied w/ my results, at least until my dad buffs it for me.