OK, you can know that you're not, if you still have any bits of greed, aversion or ignorance. The definition of enlightenment within Theravadin Buddhism is very simple: it's a person who is totally free from greed, aversion, and ignorance of reality. So, as long as you've got some desires, some aversions, some delusions, or whatever else, as long as you are attached to the eight worldly dhammas, positive or negative, then you are not going to be enlightened.
Now for those of you that don't know, Theravadin Buddhism does teach that there are four levels of enlightenment. So full enlightenment is totally free from greed, aversion and ignorance. But the other three levels are not totally free. So that's not quite as clear. The people on the first two levels, by definition, can still have sensual desires, still have kids, still get married and so on. On the third level, those sorts of desires disappear, and on the fourth level, everything has gone totally, on the physical and the mental level of desires. So there are different levels, but as to full enlightenment, it is whether you are still free from greed, aversion or ignorance of reality.
From what we have read, on the other levels, you will also know if you are there or not. If you are partly enlightened you will know it. Nobody has to come up to you and say, "Now you've made it". This is a nice thing to understand, because there are some teachers who are going around and doing just that. Telling people, "You're now partly enlightened". Usually this is just because the person had a bit of a concentration experience. So, according to what we have read, you will actually know, nobody has to tell you.
Now, I will put a little caveat on that, in the sense that one story here in Thailand is about a teacher who is long dead now. While they were alive, according to the story, the teacher claimed that he realized one day that he was fully enlightened. No big flash, no nothing, he just realized one day, "Oh, for a long time, I haven't had desires, aversions, whatever, I am fully enlightened." Now, that's a story in Thailand. However, Rosemary and I met this teacher and when he finished giving a Dhamma talk, he collapsed in his seat, one young monk put a cigar in his mouth, another young monk lit it up, and he went "Ahhh", like that. So you may hear other stories from other sources, but I personally saw that teacher, we listened to him teach, and stayed there for a week, and I don't believe wanting a cigar right after you are done giving a Dhamma talk has to do with enlightenment. To me it is a sense desire. So you can take that for what you want, but by definition a fully enlightened person is free from sense desires, in particular, and all desires.