You can make reservations online through Disney's website or you can call 1-407-WDW-DINE. Online is much faster.
If you want romantic and intimate, the very best place to go is Victoria & Alberts (Grand Floridian Resort by Magic Kingdom). It's the only AAA 5 diamond rated restaurant in central Florida and it ranks in the top 50 in the US. We've dined here many times and it's fantastic. There is a dress code, jacket (tie optional) for men and women should wear a dress or a dressy pantsuit. Prices for this meal are very reasonable for the quality of food and service received, especially in comparison to equally ranked restaurants across the US.
Below V&A, I rank the upscale restaurants at the Swan and Dolphin hotels (Epcot resort area) higher than any of Disney's restaurants. Because these restaurants don't participate in the dining plan, they cater to a more adult palate. My personal favorite is bluezoo because we enjoy the seafood entrees and the lounge here is phenomenal. Il Mulino (Italian) and Shulas (steak) are also wonderful choices at these resorts.
Out of the Disney restaurants, I think Citricos (at Grand Floridian) has the best combination of food, adult atmosphere and service. This is as close to "intimate" as you will find at a dining plan participating restuarant. I think Jiko (at Animal Kingdom Lodge) has a nice atmosphere but the food and service are not quite at the notch of Citricos.