Grapeshot & Samum bombs can both be used to destroy nests...
You start with both of these recipes and can craft them yourself (you do not need a craftsman) once you find the materials. You can loot/harvest the materials in the starting area but saltpetre is not common however if you can buy it from a herbalist. Once you have crafted the bombs you can use them to destroy nests simply by pressing the action button/key when near a nest and Geralt will light and drop one in resulting in the nest exploding and you being rewarded with XP for destroying it a few seconds later.
Be sure to stick around for after the explosion as the monster nest usually drops valuable loot and crafting components.