To easily evolve Eevee into Espeon/Umbreon, do the following steps below or check out the video to increase your Eevee's happiness as much as possible:
1) Catch an Eevee on Route 10 with a Luxury Ball, purchasable from the Pokeball Boutique in Lumiose City. 2) Get the Soothe Bell from the old lady in Shalour city. 3) Feed Vitamins like Carbos,Calcium etc to your Eevee. 4) Use Potions on your Eevee. 5) You will randomly come across Soothing Bags in your journey. Tap it 100 times with your Eevee and it will increase the happiness. 6) Walk with your Eevee in your party (in any slot). 7) Make your Eevee win battles by defeating easy trainers and pokemon 8) Give your Eevee massages from the lady in Cyllage City. 9) Level up your eevee and evolve Eevee during the DAY for Espeon or NIGHT for Umbreon.