How are gravitational wave formed?

Answer 1

By accelerating masses.

Answer 2

According to "General Relativity", gravitational waves should usually be formed when masses accelerate.

See the "related links" below.

For the second link you will need to scroll down the headings on the right of the page then click on "Gravity Waves". It's nice link, but there's perhaps too much detail. Just use what you think is helpful.
Gravitational waves usually form whenever masses are accelerated.

However waves are not formed in some cases, in particular if there is spherical symmetry.

This is a difficult thing to explain. It involves predictions from Einstein's "General Theory of Relativity".

You can try the "Gravitational wave" page on Wikipedia. Don't worry if you can't understand it all, but it may give you an idea of what is going on.

Also, see "Sources and related links" below.