I currently work in a small office, just me and my direct supervisor. I'm expecting a job offer from another organization in the next few days and wanted to prepare myself in case I have to give notice. However, my boss has been out of the office for a month now on vacation and with health concerns and has not communicated with me much during his absence, just a few text messages here and there with no specific information. I have no idea when he'll return, and even before his time away he tended to show up and work very random hours. I really have no idea how to approach this.
If your boss is unavailable, then you send your notice to their boss, cc'ing yours.
If your boss is the owner of the company, and therefore there is no one above them, then you send the notice to the person running things in their absence.
If there is no one running the company while the boss is absent then you just email / text the boss.
Worst case: If it is impossible to reach anyone, you send your notice by registered mail to the company address. If the company isn't able to receive the notice, that's their problem, not yours. Imagine the Inland Revenue asks the company for a payment, or the boss is asked to appear in court for some reason. Do you think they'll wait just because your boss decided to go on holiday? They won't.
Send him an email giving him the notice. Tell him him that you are available for a conversation on the subject any time. If he wants to contact you and talk to you, he knows where and how to find you. At least, until you're gone. Follow up your email with a voice mail in case your email gets snagged by the spam filter of his Inbox. If you have an address for your boss, send him your notice by snail mail, too, by registered mail. The whole point of this exercise is that you are not taking any chances on him not getting the message you're giving him.
If your company has an HR and/or the company has produced an employee manual, review the way you're giving notice, which right now is by email, against their accepted procedures - You don't want anything to stand in the way of your exit. And since your exit is your last official act at the firm, you might as well make sure that you're handling it properly.