Disconnect the wider yellow cable first. There are ears on the side of the connector that you have to push to release the cable.
The smaller black/brown cable has a connector with a clasp. Lift up the clasp as shown in the picture to release the cable.
Next you have to remove the spring for the umd door. The white square part holds the spring in place. Use your flathead screwdriver to pry it out.
The part of the spring circled in green slides into a hole in the umd door circled in red. Push the umd door part in the direction of the arrow and push the spring backwards until it pops out of the hole.
Take the UMD cage off the frame as shown in the picture.
Flip the PSP over and pry the door out with the flathead screwdriver.
The umd door removed with umd cage attached.
Before you replace the umd drive check the two switches shown in these pictures. They control the umd drive. If one is broken your umd drive will not work.
Remove the four screws shown in the picture. They have rubber boots which you may need to reuse in your new drive.
Remove the old drive. Installation is the reverse of removal.