Register with the electric company if you have critical medical needs. Being registered can put you on top of the list when the electric company works on restoring power.
Have an emergency plan. Have someplace to go that you know will have power, or perhaps consider installing an emergency generator.
Assemble an emergency kit. Know what medications you need and have fluids available to hold you over.
When the outage hits:
Report the outage. Have the telephone number handy for the electric company when your power goes out.
Unplug major appliances. This will protect these devices from a power surge when power is restored.
After the outage:
Seek service credits, if available. Depending on your utility company's policy, you may be entitled to service credits and other compensation should you suffer through a prolonged summer power outage and deal with inconveniences like spoiled food in your fridge.
Can you sue? You'll probably only be able to sue over a power outage if the electric company or your landlord was somehow negligent or careless in causing it. Generally, acts of nature like a storm or heat wave will not entitle you to any damages for a summer power outage.