I'm guessing that you have the original rear brake shoes on the car. The
drums are probably rusted on. They should be able to be removed by hand,
a puller is not normally needed. The brakes are only actuated by a cable
when the parking brake is used. Normally they are hydraulically actuated
using brake fluid.

The squeal may be coming from the normal contact points of the shoe
against the backing plate so when you brake, the shoes move slightly and
they squeak. The contact points are usually lightly lubricated with a
grease, (I've been using waterproof) that has probably been washed off
and rust has formed on the surfaces.

If you don't know exactly what you are doing, as this is an extremely
important safety issue when disassembling and reassembling, I would
strongly suggest you take your car into the Toyota dealer and have them
diagnose and repair the problem.