To shatter enemies you have to freeze them and then kill the enemy while it is frozen. There are certain skill gems that can apply the freeze effect as well as support gems. Here is a link to the specific gems in the wiki:
https://pathofexile.gamepedia.com/List_of_freeze_related_ski...Your best bet to do this is to get an AoE spell gem that can cause freeze, I personally reccommend Cold Snap as it can be gotten early on (Act 1 if you are a Witch, Templar, Shadow, or Scion). After aquiring such a gem keep using it on groups of mobs. Sooner or later you will manage to freeze 5 enemies at once and if you do enough damage to 1-shot them or kill them before the freeze wears off they will shatter.
Update: As suggested by MushaConvoy, using a Hatred aura, Herald of Ice, and Ice Bite will increase the chances of freezing enemies drastically.