Unplug the record player. Be sure there is no power running through the machine when removing the needle.
Lift the arm up and examine the needle to determine if you will need tools. Some record players require you to take out a small screw in order to remove the needle. If you have this type of record player, the screw will be located right at the end of the arm. Other types of record players have a needle cartridge that can be removed with your hands.
Take a screwdriver and remove the screw if you have this type of record player. After the screw has been taken out, just pull on the needle and it will come out. If your record player has a needle cartridge, grab both sides of the cartridge and pull it towards the end of the arm. Cartridges can be removed without much pressure.