Here you can find out about the different ways of testing done at this moment as well as their reliability.
The tests currently being used in hospitals and other facilities are to see if somebody currently has COVID-19.
These are done by taking a swab of the nose or throat, which is sent off to a lab to look for signs of the virus's genetic material.
The other type of test governments & people wants to use is an antibody test. These are done to see if someone has already had the virus.
They work by looking for signs of immunity, by using a drop of blood on a device, a bit like a pregnancy test. These tests are yet (April 15th) still very unreliable.
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image from the BBC.