One of the reasons I've seen a lot of GMs shy away from personal plots for PCs is because they're not sure how to handle it. I don't mean they don't know how to run the events. I mean they don't know how to run the personal plot, while keeping it focused on the PC its for and keeping the other PCs not only involved but entertained. Today I want to talk about that.
Need #1: Something To Keep The Focus
The first thing you need is some element of the plot to keep the focus on the core character. This often is a character, but it can be an item or the general tone of the story itself. For a character it should be someone tied to the PC in question. If it is some other story element, it should be something that is clearly tied to that PC (like it involves a family curse, or their best friend's inheritance.) Characters really are the easiest way in my experience, and so unless I'm doing a back story tie in plot I tend to use them first. Even with a back story tie in, I use characters a lot.
I like characters because the character that launches the plot, and has the tie in information. All you have to do then is make it so that this character doesn't trust anyone but the PC the plot is for. Sure, they can talk to the others, but since they're the ones with the keys to the big things, they make sure those keys go to the PC the plot is for.
Need 2: Something For Everyone Else
You need stuff to do for everyone else. The bigger the PC plot the more you need to have things for other people. This is another place where you can look to comic books and cartoons for inspiration. I mean, Wolverine may have a personal plot going on, but there are always obstacles that are ideal for whatever X-Men are coming along with him.
What you have for other characters can be tangential, obstacles along the way, or aspects of their own plots. It doesn't matter. The point is that while this plot may revolve around Lindsay, that doesn't mean you can have Tom, Sarah, and Mark sitting around the table bored for three hours. Make sure there are elements in there for the other PCs.
Don't Get Hung Up On Individual RP
This may sound funny, but try to not get hung up on scenes where you are RPing with one person for too long. This is dangerous when doing personal plots because those scenes are important to the plot and so your natural instinct is to stick with them. However, if you're exclusively focused on one player for too long you're going to lose the other players. The idea is to have a plot for a specific PC - ideally all PCs should have their own plot - not to bore everyone at your table with the exception of the one having the spotlight time. So keep the focus shifting. Make sure everyone has fun.
Keep Your Metaplot In Mind
Just because you're focusing on a personal plot doesn't mean the major/meta plot for your game goes away. This is a good thing to keep PCs not involved in the personal plot entertained. Just move things along. Keep everything moving. Your game will have a stronger sense of motion and depth to it.
Experience Will Teach you
Juggling multiple plots in one session, and separating the PCs for parts of a session is tricky. You'll get better with practice. The key thing to remember is to keep switching which player you're focused on every few minutes. I try for 5 minutes at a time, but sometimes you can't do that. Don't beat yourself up over it. Just learn and do better next time.