nai_cha: What you're describing is a pretty common scenario for people who are older (and have more RL responsibilities) who play D&D. Unfortunately, there's not a "common" solution, because every group is different.
Some groups can just hand off the character sheet to someone else. This is great for keeping that character involved, but unless you have another person who knows their sheet very well, you just doubled someone's memory load. I don't really recommend this, honestly - even for serious gamers, it's difficult.
You can create "simple" companion characters for people who may be absent often. This is a great idea, in theory... but in my experience, while it alleviates some (not all) of the load on another player to play two PCs, it requires a LOT of prep. You have effectively two character sheets for one person, both of which need to be kept somewhat up to date. If you are a great planner, and YOU (as the DM) are the one with lots of extra time, that can work: otherwise, it's about the same as the first option.
Some people "hand wave" it. This is definitely the easiest solution, but the downsides here are that it can dramatically change your combat encounters depending on who left (if the leader disappears, you will see a much bigger impact than if it's the 2nd striker). This is something you CAN work around - by adjusting combat on the fly - but it's difficult. And frankly, it once again helps to plan ahead. "Oh, he disappears for a moment - and suddenly there's a rock slide that kills two guys!" You have to adjust combat significantly, and sometimes (like against one solo) that's really hard to do. ALSO, it's not ideal for RP-situations either, since maybe the person who left has a key piece of information or insight in-game.
The "running gag" or "dimensional warp" approach is basically hand-waving but with a slightly more detailed reasoning. It suffers from the same drawbacks, and additionally it can get old after the 10th time someone runs back from the bathroom.
As an experienced gamer, I have tried all of the above solutions. Ultimately - and this is the bad news - there's only one solution that works with 100% of the situations, 100% of the time: shorten your playing time. It sucks, but no matter how you "make up" for the fact that someone missed part of a session, you're still going to lose time explaining to them what happened, and most importantly you're going to lose part of the human interaction that makes D&D so much fun in the first place. If Joe comes in 30 minutes late and finds out you guys just finished a raucous RP session that will spawn dozens of in-jokes for months to come... well, that sucks. So unfortunately, the best possible solution is the one that hurts the worst: reduce your play time by 30 minutes so that Joe can be there.
Believe me, I know it sucks: we love playing D&D, it's HARD to get games together, and the worst solution is always one that reduces the amount of time you can play. And clearly this won't work for everyone, because some people will just never go there. But that's really the only way to keep everyone involved the entire time. And D&D is about the group: it's about interacting with friends. Without that: why are you playing?
Sorry to break the bad news, but as I said I've tried all the ideas mentioned so far and this is the only thing that actually works. It means less D&D, but I think it also means more quality D&D when you have it. Personally, I have accepted it as one of those things you have to do to be a grown up.
