How do I evolve Eevee into Leafeon or Glaceon in Sword and Shield?

Previous games required an Eevee to be levelled up while near a Mossy Rock or an Icy Rock in order to evolve it to a Leafeon or Glaceon, respectively.

Where do I find these two overworld objects in Sword and Shield?

Solution 1:

Leafeon and Glaceon's evolution methods have been changed. Leafeon now evolves by Leaf Stone and Glaceon now evolves by Ice Stone.

Umbreon and Espeon evolve through night and day as they did before, however it's worth mentioning that they evolve depending on what the actual location's sky is doing -- some towns have a fixed time of day, and the evolution will reflect that, even if it doesn't match up with the real world time on the Switch console itself.

If you want a Sylveon, it needs at least 160 friendship/affection and to know a fairy-type move. If you want an Espeon or Umbreon, it needs at least 220 friendship/affection and must not know a fairy-type move. See this answer for more information on the changes made to friendship/affection.

Solution 2:

Use the evolutionary stones to evolve Eevee in the evolution you want, as these overworld objects are not there (source). Quote (emphasis mine):

These special boulder-like rocks were included in multiple generations of Pokemon games, but they do not appear in Pokemon Sword and Shield.

Since neither the Moss Rock nor the Ice Rock appear in the Galar region, how do players evolve Eevee into Glaceon or Leafeon? Well - players simply need to use a Leaf Stone to evolve Eevee into Leafeon or an Ice Stone on the Eevee to get it to evolve into Glaceon. These evolutionary stones can be found in the Wild Area, along different routes, or appear as items that the Digging Duo can collect during their periodic digs.