One of the only times I have felt like a spy was when I was job searching while currently employed. You feel like you're a double agent. You're always searching for new leads, you need to pledge loyalty to both sides before jumping ship, and you need to conduct your operation under the radar. If you get caught, it's all over.
Avoid shared devices. Whenever possible, do the majority of your job hunting at home and on your own devices. And, without question, using your own email addresses. If you absolutely need to respond to queries, do this on a mobile device like your smartphone and tablet. I'd recommend uploading a copy of your resume and any other presentation materials to a shared system like DropBox or Google Drive. That way you do not need to download these files onto your work computer. You never know who might have access to your computer or how much your IT department is looking into the email you are sending from the company server. It is not worth it to test the waters.
Legally, anything you download on a work computer is the company's, not yours. Naturally, you want to only be job searching off the clock. But what if your dream job emails you and needs a response ASAP? In these cases, emailing during office hours is essential.
Attire matters. If you usually come into the office looking like you crawled out of bed and then suddenly show up in a pressed shirt and a blazer, people will notice that something is up. Make it a habit from day one of your search to always dress as if you have a job interview. You'll throw people off and even start looking the part in your current job. Keep this in mind for shoes as well. If you typically arrive in the office in duck boots and flats and then leave mid-day in heels...the jig is up. Either change into work shoes before you get into the office or vice versa. Don't give your manager a reason to doubt you.
Time it accordingly. Loyalty matters at whatever company you're working at as well as the company you are applying to. Do your best to arrange your interviews before work, on your lunch hour or after hours. Your interviewee will be empathetic to you and understand that you are trying to be fair to your current boss.
If it is absolutely imperative to meet during the day, go in for the meeting, but make up that hour or two of missed time to your current employer. Stay later or come in earlier if you have to. If you know the interview will keep you away from the office for more than 1.5 hours, it would be wise to take PTO. You can typically ask your hiring manager how much time you should allot for the interview. If you are meeting with four people, it's safe to say you should take PTO.
Excuses, excuses. People always ask me, "I have an interview during the day – what do I tell my boss?" I hate lying and think that honesty is always the best policy--except when you're looking for a new job. There is no correct answer here, but if you work in a role that normally keeps you in the office from nine to five, then you need to get creative with your answer. If you are dead set on interviewing and finding a new job, chances are you'll be interviewing plenty, and saying you have a weekly doctor's appointment isn't going to work. Instead, you could say you have a physical therapy appointment. Other ideas include a colleague that is visiting from out of town or networking. The less you say, the better.