In the Scrum methodology it merely affects estimation.
You would assign focus factor for that person based on the allocation of their time to each project.
So, if I am working on Project A and Project B equally, Project A would calculate resources like so:
Project A — Team focus factor of 70%
Sam - 10 days, 100% allocation (7 after focus factor)
Joe - 10 days, 100% allocation (7 after focus factor)
Me - 10 days, 50% allocation (3.5 after focus factor)
Total: 25 days * 70% focus factor = 17.5 projected velocity
You might also calculate focus factor separately for full-time team members and for part-time team members rather than once for the whole team, due to reduced efficiency from splitting projects. In this case, you'd use my project focus factor of 50% and multiply it by a personal allocation of 50% for 25%, or 2.5 days projected velocity.
How well this works in practice, is going to be a factor of how well you know in advance how much time a shared resource is going to spend on each project, and how well Scrum is working for you in other ways.