Decision to Amputate
After opening the door with the key you found in the lizard statue, a small computer will start playing a recording from the Origami Killer asking you to amputate your own finger. However, deciding to go through with it is up to you. If you do not want to amputate your finger, simply walk out of the room to continue the story. Otherwise, you will need to continue and make preparations for the surgery.
Amputation Tool
There are several items in the room that you may choose to use to cut off the finger. On the floor next to the TV stand is an axe, a knife is in the wall in the kitchen, a pair of pliers is in the TV stand behind the table, a saw is on the floor beside the table and a pair of scissors is in the bathroom sink. All of these will work and the only difference is the PlayStation trophy you will get.
Additional Tools
In additional to finding a tool to cut off the finger, there are some additional items you may want to use. In the medicine cabinet in the bathroom there is disinfectant that you can use before and after the amputation. A flask of alcohol is in the kitchen cupboard which you can drink before you cut off the finger. You can bite on a piece of wood from the rubble pile under the window while cutting of the finger. Finally, you can use the piece of reinforcing bar next to table to cauterize the wound if you heat it on the stove.
Amputation
Gather the items you want to use, then sit down at the table. You will be presented with an option to try out the motion and an option to actually go through the operation. Wait until the character slows his breathing, then perform the gestures displayed on the screen to cut off the finger. After your character gets out of shock, you can use the disinfectant and the rod to cauterize the wound.