I feel really stupid asking this question but do you have to push the brakes to start the 1986 trans am. I recently got the car from my mother and I want to try and get it up and running. Every time I try to start the car it makes a click noise and a red light that says brake pops up and I can't start the car

No.

Is the battery dead?

No, but it's a good habit.

The battery light coming on at key-up is normal, and show's you have a little battery voltage, but perhaps not enough to crank the engine (causing a clicking noise from the start motor solenoid).

hook up a battery charger..

No, you Don't have to press brake to crank. You have a weak battery or a poor/bad cable connection. Wiggle the terminals at the battery and see if that helps. Take cables off battery and clean terminals and post. Put a battery charger on battery.

Unscrew & re-install the Ground wire leading away from the battery ternimal and gets screwed to the body right next to the battery,.........