Step 1: Give Eevee a soothe bell. This item is found in National Park on the top right. It will double his/her happiness when you do the following things:
Step 2: The hair cut brothers in the underground tunnel in Goldenrod will make eevee happier. They do it once a day, the ace trainer is better, and the bird keeper is decent but not as good. Do this daily.
Step 3: If you have unlocked Kanto, smash lots of rocks to get shards, and there's a man in Fuschia city who will give you certain berries that increase happiness. If not, you can walk with eevee a lot. Every 300 or so steps it will get a bit happier.
Step 4:To check eevee is almost reasy to evolve, go to the house in the middle-right (you'll see a school kid), and talk to the woman in the pink shirt. If she says, "It looks really happy!It must love you a lot." you know you're ready. Go ahead and level it up.
Step 5: Vitamins work well, but they're EXPENSIVE. I don't really reccomend them, but if you've gotten some rare candies, they work.