Yes, you can, and into all 7 evolutions as well. Flareon/Jolteon/Vaporeon are through the use of stones like normal that you can buy once a special shop comes to you. Umbreon/Espeon/Leafeon/Glaceon are a bit different, some of them evolve once their stats hit a certain number (ex. Eevee has to have a minimum 94ish defense and then finish a battle in the grass city to evolve into Leafeon), others depend on the link % (ex. Eevee has to have I think around 70-80% and then finish a battle in the psychic city to evolve to Espeon. Don't quote me on the exact numbers).
Right now I have a Vaporeon and Flareon, Hoping that eventually enough Eevee will show up for me to get more!! I would strongly suggest getting Vaporeon :D