Slugs and snails are everywhere, and no one tries to eradicate them from their whole garden (and in my experience "slug damage" is more often caused by snails). There are only a few plants they do serious damage to. So rather than eradicating the entire slug and snail population, we aim to protect those few vulnerable plants, such as vegetable seedlings.

How you do it is a matter of taste. A regular scattering of slug pellets during the vulnerable period is very effective. Unfortunately pellet-poisoned slugs make birds and other animals who eat them ill. So some people don't like using the pellets. There are some less damaging chemicals avaliable, but they are generally more expensive and less effective. I have found that a mulch of used coffee grounds is effective in protecting one especially vulnerable plant. Some people swear by beer traps. etc. etc.