Fuel Gauge and Speedometer

I got two problem with my 1982 Caprice.
1. No matter how much gas I got in my car the gauge is always on the half way. How do I fix this?
2. My speedometer doesn't display the right speed. It doesn't matter what speed I'm driving at the needle on my speedometer will move back and forth. How can I fix this?

#1. Replace fuel sending unit located in tank.

#2. Lubricate the speedometer cable (internally - this requires removal of the instrument cluster). There is a post made by me a couple of months back that details how to perform this. Also, make sure the tires on the car match the placard in the door sill.

How would I replace the fuel sending unit?

It involves removing the tank from the vehicle. A Chilton's or Haynes manual will detail this for you.

Drop the tank by unbolting the straps. Disconnect the two hoses and the sending unit plug. Once the tank is down, use a flat screwdriver to turn the lockplate that holds the sending unit tight to the tank counter-clockwise unil the tabs reach the openings, allowing the locking plate to come right out. Using the metal lines coming out of the sending unit as a handle, pull the sending unit out of the tank. Replace the big O-ring and drop the new sending unit in. Follow the instructions now in reverse with the locking plate, plug, hoses, etc.