Very discreetly.
First you need to be clear in your thinking about why you want to change jobs. If you still think you want to look for another job, then your behavior has to be modified so as not to jeopardize your current job situation while you get ready to start marketing yourself to potential new employers.
It's very important to look closely at how you interact in your relationships. Do you really want to broadcast to the world on social networks that you are looking for a job? Imagine that if you are online and posting personal information about yourself, people on your job are reading about your adventures and desires. Do you really want to out activity that should remain private until you are ready to share it with the world?
You will need to figure out how to start toning down or backing out of sharing so much info about yourself. If you are used to dressing grungy or overly casual and suddenly you start to dress more corporate or fittingly or creatively for your potential new job, you are going to cause some talk and suspicion.
Also as you network around and add names of recruiters and head hunters to your call list, some assumptions are going to be made by everyone who knows you.
The best thing to do is to work with a mentor of your choice who will back you up in your efforts or slap you down, when you feel too full of yourself. Once your mentor(s) are in place and you have their trust and vice versa, you can start reinventing yourself, beefing up your resume and making contact with individuals who will help you work through your career growth.