Two words, Kristi. One is bean. As in, L.L. Bean. The other is: Cabela's, otherwise known as the Shrine to All Things That Involve Hooks, Bullets, and Arrows Used to Snag Scaled/Furred/Antlered Creatures. At either place you'll find reliable, tested fly-fishing gear that won't break the bank, unless of course you want it to.
Examples: L.L. Bean sells a set called the Streamlight Fly Rod Outfit that is available in a variety of lengths and weights to suit all sorts of fishing. Most useful is probably the six-weight two-piece rod, which comes with reel, line, and case. Price: $189 (www.llbean.com). Over at Cabela's, you'll find the Fish Eagle rod/reel combination, an eight-foot two-piece pole with line and backing (no case) for the even better price of $130 (Christmas rush—they're currently sold out; www.cabelas.com).
So there's your basic setup, although of course it's just a start. Flies you can pick up at any fly shop based on what the fish in that area are after. You'll need a net, such as the Scientific Anglers Magnetic Release Net ($35; www.llbean.com), which uses magnets to attach the net to your body so it doesn't flap around. A good fishing vest is always handy—Bean sells what's called the West Branch vest for men or women for $59. Waders are up to you; it depends on how cold the water is and whether you want to fish from the bank or not. Grippy shoes certainly are handy, though. Henry's Fork Wading Shoes ($129; www.orvis.com) are like a light hiking shoe that can take repeated soakings and have felt soles that stick to slick rocks.
That should get you (or your undisclosed giftee) started. Fly-fishing is like any other hobby: You buy a few basics, then before you know it you're poring lustfully through catalogs and websites, looking for the next thing to buy. It's a sad addiction, but a fun one!