You need to come up with a credible reason to convince your boss into giving you some time off from work. Being honest with the boss is your safest bet, since he may investigate whatever reason you give him. Reasons such as taking care of a sick loved one or a scheduled vacation may work for you. There is no need to share the details of your vacation with your boss, as it is something personal.
Like any other professional dealing or request, it is best to put your leave request in writing and sending it to your boss for his approval. This will serve as a proof in case your boss forgets or denies giving you the time off. In most officers, the communication between employees and the management takes place via internal email server. If you have such setup in your office, use it to mail your request to your boss. Make sure you mention the date and reason clearly in your email.
Forward your leave request to your boss as soon as you become aware of the need to take time off from work. Delaying it until the last moment can greatly hurt your chances of successfully getting the leave request approved. Do not think that if you ask the boss for time off at the last minute, he will have no option but to approve it. He is the boss after all and therefore he can take any decisions he sees fit.
Approaching the boss to ask for time off from work at a certain time during the day can be great for you. It is best to avoid the start of the shift to approach the boss, as there is a whole day of work and tensions in front of him and the last thing he would want to hear is one of his employees asking for a time off. Also choose the right day of the week. Mondays and Tuesdays should be avoided, while Thursdays and Fridays should be preferred.
Giving your boss an incentive to approve your leave request can make a huge impact on his final decision. Offer to do extra hours before taking the time off or returning from the holidays to make up for the days that you were missing from work. You can alternatively suggest some other solution such as getting your colleague to do a bit of your work.
If your boss denies your request for time off from work continuously, you can toughen up your approach and simply inform him of your unavailability on certain dates. He may find himself stuck with no other option but to approve your leave.