Step 3: Remove the Socket's Inner Components
Once the head of the socket has been removed, you'll see that the inner components are (basically) secured within the socket by pressure.
Remove the electrical connection part of the base (the black plastic part that makes contact with the bulb) by simply pulling it outwards with your fingers.
Then, use a slender screwdriver (or similar instrument) to pry the rest of the components out. The white tabs through which the wire feeds are held in place by pressure against the surrounding socket. They should come out with a combination of prying & pulling. Shouldn't be too difficult.