As per other answers, it is usually marked with the ⌀ symbol on the front and, if not, on the barrel. Some specialty lenses do not accept filters, in which case you won't find any markings.
For your lens, the thread is 67mm
This is the thread size which means you can attach that size of filter directly. This convenient but costly. Instead, I buy my filters in the largest size (77mm usually) and have step-up rings to bridge the gap. A step-up ring costs about $12, so if you buy 77mm filters and have a 58mm, 67mm and 77mm lens, you need 2 step-up rings: 58->77 and 67->77. The only catch that you can't use a step-up ring and a lens hood at the same time. It saves lots of money considering a good polarizer costs over $200. Even if you have just two lenses with different filters you'll save. My lenses have 8 filter sizes so you can imaging how much money I saved on polarizers alone!
There will be a degradation in image quality if you use a filter. See my answer to this question. Generally, the less you pay, the more degradation there will be. UV filters are usually sold for protection but polarizers have a genuinely useful photographic purpose, attenuating glare, surface reflections and increasing color saturation of the sky and some other surfaces as a side-effect.