look at the inside of the lens cap, filter thread size already stated there.
My lens hood is always on, day or night, once the camera is out of the bag, the only time I remove it is when I have CPL filter on or it gets in the way when I need to shoot very close to glass window.
as mentioned.. you can find the size of what lens filter to get on the lens itself.
if you buying filter.. bring the lens and get it fixed in the shop.. Better that way..
As for lens hood. I leave it on everytime. Like what Catchlight says. The only time i remove it when i have a CPL filter on or when the lens hood really gets in the way..( for some lenses.. the lens hood can be big )