I've emailed them to my home email address, but depending, you can usually find a MODEL SPECIFIC cable to connect to your computer's USB connection. It usually comes with a Software program that lets you connect your computer to the phone and simply transfer the Photos, add ringtones, download your address book or phone numbers from your phone for safekeeping.
If you're starting from scratch, the fastest way is to simply send it via email. You have to create an address/phone number listing in your new phone for you first though.
Did you get one of the Galaxy models? Which one?
I'll show you the example for a Galaxy S2
Steps for transferring pictures and videos to your computer from your Samsung Galaxy S2 -1. Open settings2. Click on ' Wireless and Network '3. Now click on ' USB utilities'4. Click on ' Connect storage to PC 'After performing these steps, a window pops up asking you to connect USB cable to use mass storage.DO NOT CLICK ON CANCEL.5. Connect the transfer cable to computer.The screen should now show ' USB connected'6. Click on the ' connect USB storage ' button at the bottom of the screen.A folder called ' NO NAME ' should show up on your desktop.7. Open folder called ' NO NAME ' on desktop.8. Open ' DCIM '9. Open ' Camera 'You can copy the photos and videos from here or import them