Depends on what kind of phone your old device was. If you can connect your old device to your computer then you may be able to extract the contacts from the phone and then sync them to your iPhone (example would be Blackberry devices...you can use the DeskTop manager to do this). You may be able to get VZW to do it in-store...you would have to check with them. If you have an SD card on your old phone you may be able to simply plug your card into your computer (assuming you have an SD slot on it). These are vague answers but you can easily just do an internet search for whatever device you had and how to transfer contacts from it to the iPhone 4s. You will usually find sites that give great detail on how to do it.
Congratulations on your new iPhone 4S! You've made a GREAT choice! I'd also like to thank kaebfly for the feedback & suggestions.
I want to include a link titled "Activating and Setting Up iPhone 4S and iPhone 4 8GB - Existing Verizon Wireless Customers", which will include instructions how to transfer contacts using the VZ Contact Transfer app (if you had a previous Backup Assistant device) & instructions for contacts syncing with your computer/MAC & Google.
I hope we have answered your question, and have addressed your concern.
Follow us on Twitter @VZWSupport