How can I become a mysterious person?

Know when to speak. how did Plato put it?" wise men speak because they have something to say; fool because they have to say something."
Be the wise man, not the fool.

Be confident. confident enough to not have to fill in the gaps in conversations. It's also about not being rattled by the natural silences that crop up in day-to-day interactions between people. To be successfully mysterious, you need to come off as needing nothing from no one.You don't need approval and you definitely don't need anyone to hold your hand through any endeavor.

Be a brilliant summarizer but not much a good detailer. Never give away too much when you're talking about personal things. For example, if the person you're interested in wants to know about your past, be very candid but not specific. Never tell this person extra details, or give the whole story. Work on your summarizing everything. When you're answering questions, you answer them simply and to the point, no dilly-dallying about it. The other person won't know whether to probe or not, since you gave the whole story (even though it was with such little detail). How can they argue with what you had to say? What right do they have to the details? Most people will not want to tip-toe the line.

Maintain a calm exterior at all times. Avoid showing over-emotional reactions to events or people. Calmness is linked firmly to exuding confidence and a calm reaction will confirm that you're level-headed, as well as eliciting an aura of mysteriousness. People will wonder how you can manage to maintain to remain so calm about situations in which they're shocked,outraged, or panicking. When showing emotions like anger or love, be stoic and composed. Show emotion with your eyes,rather than your mouth or facial expressions or actions. Don't yell if you're angry about something, and don't jump to kissing someone if you think you're in love. A lover would be expecting both things, so don't go for the obvious reaction. Train yourself to be calm and reflective. Keep your voice calm and relax.
Develop your OWN STYLE.

Be Unreadable. "oh , i was just thinking" or " i was just wondering about something," or " I've just been reflecting over
If someone asks you a questions, feel free to answer it literally. "what are you doing?" can be followed with, "talking to you" or "sitting on a chair". You don't have to play into certain social norms if you don't want to. As long as you find it funny, you'll be able to pull it off.

Be polite and considerate,not Aloof. Keep your sense of respect and compassion for others; being mysterious is not about being superior than others. It's more about leaving things not said, and showing others that you value your privacy and space. There will be people that don't like this side of you. So what? If they're not comfortable with it, it's their problem. But if most people don't like it, you may want to consider how you're coming off.
:)