I can only pick up more obvious sarcasm. Like if it's something that of course would not be said seriously, such as " How wonderful! I just cut off my left pinkie while chopping vegetables!" Now that's an exaggeration, of course. There's also tone of voice. An overly enthusiastic tone can indicate sarcasm, but sarcasm is also expressed in a very serious tone of voice, probably for effect.
Now, with people that I know very well, it's much easier to pick up on sarcasm. I know their habits, speech patterns, and the way that they think. So I have a lot more information to go on. Even then, with certain people I have trouble with subtle sarcasm and I have to ask "Are you being serious?" This happens on a daily basis, unfortunately.
In public, with strangers or acquaintances, I have a much harder time. I often don't get jokes when presented in a serious manner, or sarcasm either. It's embarrassing at times. I'm not sure how to deal with it, to be honest.