There are many things that you can garden with naturally that will rid your garden of slugs and snails.
There are natural predators. Called nematodes, that are almost invisible and creep around your garden and attack them.they crawl away and die underground usually, a short while later. These can be bought online, or garden nurseries sell them.
Copper tape works well if you have any areas that can be enclosed, they get an electric shock from this, and wont cross it- the tape can be adhesive or rigid copper barrier can be used.
The diatomaceous earth works well, as mentioned, and is early cheap. I have less success with egg shells and sharp grit, but could be worth a try.
There are also animal friendly slug pellets that are now sold, which contain an Iron based compound, safe for pets and wildlife, which I use. I will find a link for you, later on.
Removing fallen autumn debris removes some of their shelter over winter, and I have far fewer now, since I meticulously clean my garden in fall/autumn (ok this doesnt help right now, but is good preventative action for next summer).
Overall, with the pellets that are pet safe, as well as the natural predators, you should be able to have as good as gotten rid of them. Remove any damp summer hiding spots too, and keep your lawns well clipped at the edges, as theyll often shelter around these, are theyre cooler and moister than being exposed to sunlight.
Hope this helps. Good luck! Rob