[noun] + こそ [noun] + [particle] + こそ [verb て-form] + こそ [sentence] + からこそ
こそ puts strong emphasis on the word before it: this one and no other. It goes straight after a noun, where English would stress the word with the voice or add "precisely".
The sentence carries conviction or feeling, so a flat statement of fact does not take こそ. In everyday speech you meet it most in こんど今度こそ, ことし今年こそ and こちらこそ.
こそ goes where は or が would have been. It is never added on top of them.
Other particles stay, and こそ follows them: にこそ, でこそ, からこそ.
When someone thanks you or apologises, こちらこそ turns it back on yourself: "no, I'm the one who should…". It is polite and fits any conversation; among friends, わたくし私こそ does the same.
These go beyond stressing a single noun. Each is also a grammar point of its own.
After a plain-form sentence and から, こそ marks the reason as the one that decides the matter.
After a て-form, こそ says that only by doing this do you get the result in the second half.
After a ば-form, こそ means the same as からこそ. It belongs to formal writing; in speech, say からこそ.