You could use your phone to email the pics to your normal email address.
You could get a data cable (some phones use a mini usb plug) but that depends on on the phone, check out the website for the phone.
If the phone has a Sim card, copy everything to the Sim card and put the Sim in the new phone.
Bring the phone to the (verizon, att, or whoever the carrier is) store and have them transfer the files for you.
Hope this will at least get you started.