You can get a birthday button at each of the parks. I think there are three different designs (two of the parks offer the same button but the other parks offer their own unique birthday button, if I remember correctly for a total of three different designs). In MK, you can pick one up at Town Hall. At Epcot, I think it was at Guest Relations inside the park. Can't remember where you get them at the other parks, but probably also at Guest Relations inside those parks.
You definitely want to wear your birthday button all day. CMs and other park guests will wish you a Happy Birthday wherever you go. Depending on where eat, you may or may not get a little birthday magic. Some places will do something special for you, others do not. I don't want to get too specific because it's more fun if you get surprised, and plus I wouldn't want to set expectations and then have you feeling disappointed if nothing happens.
I celebrated a major birthday at WDW last May and collected a button from each park! It turned out to be the best place to celebrate such a major milestone. Hope your birthday ends up being just as much fun!!