Hello, Shanon!
I suggest that you first go straight to
Walt Disney World's website and select "Places to Stay." Then, select a resort category, then a particular resort. (I've already directed you to a page where you can find this information, selecting "Value" and the first resort which appears on that list, DIsney's All-Star Movies Resort.)
On that page, you'll see the dates for the 2012 Value Season-Weekday. Just use the "Season" button on the right side of that page to find other dates, and weekend rates as well. From year to year, these seasons tend to remain the same, adjusting only for holidays, really. Value Season tends to run in January and some of February, with "Value 2 Season" running August through late September. Keep in mind that holiday weekends will not usually fall within these categories.
My first trip EVER to Walt Disney World was ten years ago, during a January off-peak season, selected specifically in this manner. We wanted to get the most time for our money, and found that this was the best time for us to do so.
Send more questions as you think of them, too. I'd love to help!