Most people have learned it the hard way at one time or another . . . NEVER leave your current job before you land your next one. But looking for a new job without getting fired is tricky. Here's a good list of do's and don'ts from Monster.com.
1. Don't tell anyone at your current job, and don't use them as references. Sooner or later it'll get around. And even if your boss doesn't care, it might strain your working relationships if other people are looking to move into your job when you're gone.
2. Keep your LinkedIn profile 100% complete. It doesn't raise eyebrows, as long as you don't write that you're looking for work. And hiring managers often go there first these days, so you should give them everything they might want to know.
3. Don't bad-mouth your current employer. In a few more weeks, the person you're sitting in front of might BE your current employer. But before that, they'll have to decide whether they like the way you talk about your boss.
4. Ask your interviewers to keep your job search confidential. Even if they don't call your old job, they might tell other people at their company . . . and maybe one of them knows people at your old job.
5. Stay focused on your current job, and schedule interviews during non-work hours. You still have to keep up your performance, so you don't get fired before you're ready.
6. Don't use any company equipment in your job search. Lots of companies track Internet and cell phone usage now.
7. Don't dress differently than normal. If you need a suit and tie for your interview, but you never wear suits to work, keep your interview clothes in your car and change after you leave the office.
8. Don't post your resume, and don't talk about your job search on social media.
9. Always be honest if you get caught. There's no reason to lie if someone finds out and confronts you. You're leaving anyway, and it usually comes back to haunt you later.