When you find a new job and apply for it, is it a common practice to tell your current employer. Do you tell your current employer that you have an interview when asked to come in to interview?
No. If you do that, they will find your replacement and boot you as soon as it's opportune for them. Never let your employer know you're looking for another job until you actually have one.
Is it a common practice to when you find a new job and apply for it that you tell your current employer or you tell your current employer that you have an interview when asked to come in to interview?
No, this is not a common practice. At least not in my part of the world.
Common practice is to use a personal day/vacation day/sick day, or to come in late or leave early - to attend the interview.
Here at least, folks would seldom tell their employer that they are interviewing. Only at the point where you have a signed offer with an agree-upon start date would you give your notice, and thereby inform your current employer.
[Note: Although it happens often in my part of the world, some would caution against calling in sick to attend an interview. As @weston points out, it's possible that you could lose your current job and any chance of getting a good reference if caught.]