First they would have to have been saved to the SIM by you. They aren't automatically saved there. Second you would have to put the SIM back in the phone it is from, then you can either move the contacts back to the old phone, from the SIM or connect the old phone to a computer via USB cord and move the files from the SIM or the Phone to a computer. Once done you can then transfer them via USB cord, to the new device.
Now if your new phone will let you insert the SIM into it and read it, you can then move the contacts from the card to the phone and then remove the SIM.