1. Is your device working in that you can connect it to your PC? If so, hook it up via USB, open BlackBerry Desktop Manager (the software that came with your phone, or download it from the BlackBerry site). Go to Switch Device Wizard and follow the prompts to back up your old phone. (If your phone is dead, you will have to skip to step 2 and manually update everything on the new device. Or if you used Verizon's Backup Assistant, your contacts should be stored there.)
2. Once backed up, turn off the old phone. From the new phone, dial *228. Listen for the prompts, then choose "activate device" (might be option 2, if I remember correctly). This should activate the other device without changing anything on your plan. If it won't activate over the air, your option is to call *611 (from a different phone number) and get help from a rep. You can also try to switch online at MyVerizon, using the ESNs, which will be printed on stickers behind your BlackBerrys' batteries.
3. Once activated, you can hook up the new device to your computer and use Switch Device Wizard to get all your settings and apps back to what you had on the previous phone.
**Edit - I see SydneyK posted more detailed instructions as I was composing my reply. Thanks SydneyK!
All you need to do is activate the new one. The other will be deactivated automatically. As far as services, since you are moving from one BB to another, they should follow.
You'll want to back up all your settings and contacts, and pictures and all with the BB Desktop manager, and then transfer them to the new phone once it is active.