You have several options. Taxi's are always available, though they will be somewhat cheaper from the Kissimmee station, as it is slightly closer to WDW (and one stop nearer Miami, too). Lynx public buses operate from a stop near the station, reaching Disney (the TTC) via a transfer at Osceola Square Mall. From the Orlando station, you have rental cars, taxi's, the various towncar companies, the CoachUSA shuttle, and Lynx again (transfer at the Downtown bus station).
Also, before you book the tickets, you may want to check Amtrak's website. Right now, a Miami-Orlando ticket is going for $6.40 online.