You should be able to put your sim in another phone, and all VM's should sync to it, and or, after your sim is in the alternate phone, press and hold 1 to take you to your VM.
You can listen to your messages from any phone including a landline.
It will varies from carrier to carrier but I believe with AT&T, you dial your number and when the voice message starts, you press the the star button. From there you just enter your password to access the menu.