Although silverfish are gross, they aren't dangerous to humans or pets directly. They are, however, dangerous to your things and your wallet. By knowing what they are attracted to and how to keep them at bay, your home and your budget will be safer.
What are Silverfish?
Silverfish are small, shiny grey bugs often seen indoors. They tend to live in dark, damp places and feed on carbs of sugars and starches.
Where are They?
Although they do like dark, damp places, they can also be found around paper, especially in your home. They can slither into tiny spaces (which is how they get the "fish" part of their name), and you'll sometimes see them in between pages of a book or inside of a framed print. They'll also get in between wallpaper and the wall or under drawer protecting sheets. They are also attracted to glues, which includes book bindings and wallpaper paste.
A clean home is the first step to keeping silverfish away. Any sugary treat left out, including small crumbs, can lure silverfish into your home in the first place. Wet spots from spilt liquid or from leaky pipes can also bring on silverfish. Once they are there, they will find any starches such as glues to keep them happy.
A way to rid an area of silverfish that isn't toxic to pets is using a home-made citrus spray. Some recipes call for lemon juice and water and are simple to make. Just spray this combination into an area where silverfish have been present, and it should keep them away.
Diatomaceous Earth is another way to keep silverfish away. It will kill them and other insects (such as ants and beetles) on contact by hardening under their shells. Simply sprinkle on the infested area (even just sprinkle onto a book bind). If there is a crack that silverfish might come from, put some into a crack. Bags of this powder can be found on eBay.
It's probably best to use this when pets aren't around. Be sure to get food grade and not pool grade, which is poisonous to pets. Food grade is not poisonous, but can still dry out an animal's eyes.
Humid climates are best for silverfish, worse for your silverfish defence. If you've seen silverfish and live in a humid climate, dehumidify your home by keeping the air-conditioner on more often and making sure to turn on fans in the bathroom after showers.