As was mentioned earlier, either sewing the sleeves directly to the vest or putting zippers in are your best options. Unless you know what you're doing with a sewing machine or have a grandma or mom willing to teach you, it's a good a idea to have it done professionally.
Remember that in attaching these things, you'll have some extra fabric (known as seam allowance) that will have to come off of both the vest and the sleeves. If you can purchase slightly longer sleeves, that's not a bad idea.