On the outside of my house I have at least one bird living in an air vent. I would rather that they lived somewhere else. I was thinking I could put some sort of netting over the vent when the bird does not seem to be around. My wife is concerned that there could be a bird's nest with eggs in there and does not want to leave the eggs to die. What is the best way to safely remove these birds without hurting them?
Go rent a shopvac, and gently suck them up. Then when you return the shopvac, they will safely place the birds outside of the business for no additional charge (as long as you don't tell them about it.)
Just kidding, if they have eggs right now then you will just have to wait. If they don't then there is a plethora of things you can do. The netting is fine, or remove the nest while it is away.
Many people have been taught that leaving a human scent on nests and eggs will lead to abandonment. But, as noted by Doresoom, the issue of leaving a scent on eggs is not a problem.
The problem is that physically disturbing the nest can lead to abandonment. Some say this varies with species and how far along in development the young are. Moving the nest to a completely new location might be too risky. It might be possible to move it slightly, but is best to avoid it if possible.
I'm with Tatton and just waiting it out. It adds some extra character to the house for a season, and the old nest makes for a cool souvenir.
Here is a video that shows and explains how to not only remove the birds but also how to prevent them from renesting in the future.