While it is not the popular answer, the best one is … very little. Most states and municipalities allow homeowner to perform basic handyman tasks in their own home. That being said, it is still risky to do most electrical work yourself.
There is a reason electricians, like other skilled workers, are extensively trained. They attend specialized school, take difficult tests to become licensed and must take continuing education every year. The question you should ask is
“Is my life, or my home worth saving a few dollars?” What is the risk you want to take? It is penny-wise and pound-foolish to skimp on something which could have major repercussions later. For example, your insurer could refuse to pay for fire or other damage if work was not done by a licensed electrical contractor.
In summary if you would not consider doing your own kidney transplant, setting up an HL7 interface or building your own rocket, you probably shouldn’t be doing your own electrical work.