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.
As far as I know, relocating the nest is not really an option for most species. Even coming into contact with the nest, which leaves your scent, can cause abandonment. You can always do more research on the specific species to see if it's known how they react.
If you try look for eggs, avoid touching not only the nest but the surrounding area in contact with the nest. A telescoping mirror is a good tool for this situation.
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.