Put your finger on top of the SIM and press it gently and pull the finger and it will bring the SIM out. If the inserting of the SIM to the phone feeled like tight fit it might require some more pressing on the SIM while pulling. Not the easiest phone to switch a SIM, that's for sure.
you did not say which model 6700 you have classic or slide. for the 6700 slide, turn off the phone, open the USB port dust cover, press the release button to remove the back cover, remove the battery, gently press the SIM holder and slide toward the hinge to unlock then swing up to remove the SIM card. reverse these steps to install card ensuring you insert cut corner first, contacts down and ensuring it is in the guide rails on both sides of the holder.