How do you upgrade your own electrical panel if you don't have the money for an electrical contractor?

You can enter an apprentice program and spend at least 6 years learning the trade. Then pass the test. Electricians are not born, they study and work to acquire their skills and if anybody thinks "HOME DEPOT" can help, in this case they cannot. Call a Pro. By the way I am not a Licensed Electrician, I was very lucky to work with Professionals and learned what my limitations are, my advice is given after 30 years of learning that engineering doesn't make you an expert.

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Open a savings account

(LIFE SAFETY WARNING! [disclaimer]

Electricity is dangerous!
You can be injured or killed!
Improper installations can cause fire, injury and death!
Are you qualified to do this work?)

National Electrical Code definition, NFPA 70 2005 Article 100 I: Qualified Person. "One who has skills and knowledge related to the construction and operation of the electrical equipment and installations and has received safety training on the hazards involved."

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Unfortunately, he is right
You wouldn't try to remove your child's brain tumor because you can't afford a surgeon. This isn't brain surgery, but can be just as deadly.
You may find that there are programs where you live to pay for this on an emergency basis, or there may be loan programs set up to help with low-interest loans.
Call the municipality where you live and ask about loans and HUD programs.
Call every charitable organization you can find or think of.
Try your church...
Barter.
Sorry, but I won't help you kill yourself.

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As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.

Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized.

IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.