Basically the answer is that naïve is sometimes spelled with the diaresis because it is derived from French which spells it that way. It is actually very *un*common for native English speakers to spell it with the diaresis, largely because, as you've noticed, the diaresis is not normally a part of the English language. English keyboards don't even contain a modifier to add a diaresis (or a tilde, accent, or any other marking, for that matter) to a letter. However, the auto-correct feature in some computer programs will change naive to naïve, as my browser has done in this post.